Metrics for VandenBroeck and Keller, Equation (20)

analyze369.0ms (1.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	75%	0%	0%	25%	0%	3
0%	0%	62.5%	0%	0%	25%	12.5%	4
0%	0%	56.2%	0%	0%	25%	18.7%	5
0%	0%	53.1%	0%	0%	25%	21.9%	6
3.1%	1.6%	48.4%	0%	0%	26.5%	23.4%	7
4.8%	2.3%	46.1%	0%	0%	27.3%	24.2%	8
5.6%	2.7%	45.7%	0%	0%	27.3%	24.2%	9
6%	2.9%	45.5%	0%	0%	27.3%	24.2%	10
6.3%	3%	45.4%	0%	0%	27.3%	24.2%	11
6.4%	3.1%	45.2%	0%	0%	27.4%	24.3%	12

Compiler

Compiled 39 to 17 computations (56.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 228.0ms

ival-div: 53.0ms (23.2% of total)

ival-mult: 42.0ms (18.4% of total)

ival-exp: 37.0ms (16.2% of total)

ival-neg: 26.0ms (11.4% of total)

ival-log: 24.0ms (10.5% of total)

ival-add: 15.0ms (6.6% of total)

ival-sub: 14.0ms (6.1% of total)

ival-pi: 12.0ms (5.3% of total)

const: 5.0ms (2.2% of total)

backward-pass: 1.0ms (0.4% of total)

sample5.6s (29%)

Results

2.5s	7709×	1	valid
2.1s	7065×	1	invalid
150.0ms	162×	2	valid
43.0ms	385×	0	valid
1.0ms	10×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 4.0s

ival-exp: 927.0ms (23.2% of total)

ival-div: 735.0ms (18.4% of total)

ival-mult: 458.0ms (11.5% of total)

ival-pi: 392.0ms (9.8% of total)

ival-log: 373.0ms (9.3% of total)

ival-neg: 325.0ms (8.1% of total)

ival-add: 303.0ms (7.6% of total)

backward-pass: 288.0ms (7.2% of total)

ival-sub: 151.0ms (3.8% of total)

const: 46.0ms (1.2% of total)

Bogosity

preprocess293.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

2270×	`sum3-define`
1954×	`fnmadd-define`
1910×	`fnmadd-define`
1778×	`fma-define`
1496×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	115
1	85	96
2	247	96
3	632	96
4	1381	96
5	2445	96
6	3749	96
7	4326	96
8	4892	96
9	5372	96
10	6040	72
11	7365	60
0	16	36
1	46	32
2	123	32
3	271	32
4	464	32
5	679	32
6	913	32
7	1218	32
8	1868	32
9	2313	32
10	3051	32
11	4744	32
12	5300	32
13	5563	32
14	6101	32
15	7504	32
0	8030	32

Stop Event

1×	iter limit
1×	node limit
1×	node limit

Calls

Call 1

Inputs
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))

Outputs

(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))

(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Call 2

Inputs

(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))

(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))) (- (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f)))))))))

(neg (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))) (- (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))))))))

Outputs
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))
(* (log (- (recip (expm1 (* (* (PI) f) 1/2))) (recip (expm1 (* (* (PI) f) -1/2))))) (/ -4 (PI)))
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))) (- (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f)))))))))
(* (log (- (recip (expm1 (* (* (PI) f) -1/2))) (recip (expm1 (* (* (PI) f) 1/2))))) (/ -4 (PI)))
(neg (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))) (- (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))))))))
(* (/ 4 (PI)) (log (- (recip (expm1 (* (* (PI) f) -1/2))) (recip (expm1 (* (* (PI) f) 1/2))))))

explain344.0ms (1.8%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
244	-	-	`(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))`
8	-	-	`(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))`
1	-	-	`(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))`
0	-	-	`(PI.f64)`
0	-	-	`(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)`
0	-	-	`(neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))`
0	-	-	`(/.f64 (PI.f64) #s(literal 4 binary64))`
0	-	-	`(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))`
0	-	-	`f`
0	-	-	`(+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))`
0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))`
0	-	-	`(exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))`

Results

182.0ms	474×	1	valid
19.0ms	16×	2	valid
3.0ms	22×	0	valid

Compiler

Compiled 434 to 50 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 134.0ms

ival-exp: 31.0ms (23.2% of total)

backward-pass: 20.0ms (15% of total)

ival-div: 19.0ms (14.2% of total)

ival-mult: 18.0ms (13.5% of total)

ival-log: 18.0ms (13.5% of total)

ival-neg: 10.0ms (7.5% of total)

ival-pi: 5.0ms (3.7% of total)

ival-sub: 5.0ms (3.7% of total)

ival-add: 5.0ms (3.7% of total)

const: 2.0ms (1.5% of total)

eval6.0ms (0%)

Compiler: Compiled 33 to 16 computations (51.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.9%	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	6.9%	(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))

Status

Accuracy

Program

▶

6.9%

(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))

▶

6.9%

(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))

Compiler

Compiled 71 to 32 computations (54.9% saved)

simplify146.0ms (0.8%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
✓	cost-diff	0	(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
✓	cost-diff	0	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	128	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))
✓	cost-diff	256	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))
✓	cost-diff	320	(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))

Rules

2270×	`sum3-define`
1910×	`fnmadd-define`
1772×	`fma-define`
1440×	`sum5-define`
1074×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	353
1	73	325
2	168	325
3	320	325
4	505	325
5	719	325
6	955	325
7	1242	325
8	1894	325
9	2334	325
10	3070	325
11	4763	325
12	5321	325
13	5584	325
14	6122	325
15	7528	325
0	8054	325

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))
(* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))
(/ 1 (/ (PI) 4))
1
(/ (PI) 4)
(PI)
4
(log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))
(/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))
(+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))
(exp (* (/ (PI) 4) f))
(* (/ (PI) 4) f)
f
(exp (neg (* (/ (PI) 4) f)))
(neg (* (/ (PI) 4) f))
(- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))
(/ (log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
(log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))))
(/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))
(+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))
(exp (* (PI) (/ f 4)))
(* (PI) (/ f 4))
(PI)
(/ f 4)
f
4
(exp (/ (* (PI) f) -4))
(/ (* (PI) f) -4)
(* (PI) f)
-4
(- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))
(/ (PI) -4)

Outputs
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/ 1 (/ (PI) 4))
(/.f64 #s(literal 4 binary64) (PI.f64))
1
#s(literal 1 binary64)
(/ (PI) 4)
(/.f64 (PI.f64) #s(literal 4 binary64))
(PI)
(PI.f64)
4
#s(literal 4 binary64)
(log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))
(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))))
(/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
(+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))
(+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(exp (* (/ (PI) 4) f))
(exp.f64 (*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64))))
(* (/ (PI) 4) f)
(*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))
f
(exp (neg (* (/ (PI) 4) f)))
(exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))
(neg (* (/ (PI) 4) f))
(/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64))
(- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))
(-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(/ (log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))))
(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))))
(/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
(+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))
(+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(exp (* (PI) (/ f 4)))
(exp.f64 (*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64))))
(* (PI) (/ f 4))
(*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))
(PI)
(PI.f64)
(/ f 4)
(/.f64 f #s(literal 4 binary64))
f
4
#s(literal 4 binary64)
(exp (/ (* (PI) f) -4))
(exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))
(/ (* (PI) f) -4)
(/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64))
(* (PI) f)
(*.f64 (PI.f64) f)
-4
#s(literal -4 binary64)
(- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))
(-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))

localize282.0ms (1.5%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 (PI.f64) f)
✓	accuracy	99.4%	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	96.5%	(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
✓	accuracy	12.1%	(-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
✓	accuracy	99.6%	(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)
✓	accuracy	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))
✓	accuracy	96.5%	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))
✓	accuracy	12.1%	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))

Results

194.0ms	238×	1	valid
19.0ms	8×	2	valid
8.0ms	10×	0	valid

Compiler

Compiled 346 to 30 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 148.0ms

ival-div: 46.0ms (31% of total)

ival-exp: 30.0ms (20.2% of total)

ival-mult: 22.0ms (14.8% of total)

ival-log: 19.0ms (12.8% of total)

backward-pass: 13.0ms (8.8% of total)

ival-sub: 5.0ms (3.4% of total)

ival-add: 5.0ms (3.4% of total)

ival-neg: 4.0ms (2.7% of total)

ival-pi: 3.0ms (2% of total)

const: 1.0ms (0.7% of total)

series208.0ms (1.1%)

Counts

13 → 144

Calls

Call 1

Inputs
#<alt (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))>
#<alt (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))>
#<alt (/ 1 (/ (PI) 4))>
#<alt (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))>
#<alt (/ (log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))>
#<alt (log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))))>
#<alt (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))>
#<alt (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))>
#<alt (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))>
#<alt (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))>
#<alt (* (/ (PI) 4) f)>
#<alt (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))>
#<alt (* (PI) f)>

Outputs
#<alt (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI)))>
#<alt (- (* -2 (/ (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))) (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))))>
#<alt (- (* f (- (* -2 (/ (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (PI))) (* 2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))))) (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))))>
#<alt (- (* f (- (* f (- (* -2/3 (/ (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))) (PI))) (* 2 (/ (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))))) (* 2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))))) (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))))>
#<alt (* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI)))>
#<alt (+ (* 2 (/ (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))) (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))))>
#<alt (+ (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (PI))) (* 2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))))))>
#<alt (+ (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* f (+ (* 2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))) (* f (+ (* 2/3 (/ (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))) (PI))) (* 2 (/ (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))))))))>
#<alt (* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f)))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* 1/2 (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* f (+ (* 1/2 (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 1/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* f (+ (* 1/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (+ (* 1/6 (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))))) (* 1/2 (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))))))>
#<alt (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))>
#<alt (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))>
#<alt (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))>
#<alt (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))>
#<alt (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))>
#<alt (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))>
#<alt (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))>
#<alt (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))>
#<alt (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI)))>
#<alt (+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* -2 (/ (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))))>
#<alt (+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* f (+ (* -2 (/ (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (PI))) (* -2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))))))>
#<alt (+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* f (+ (* -2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))) (* f (+ (* -2 (/ (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))) (* -2/3 (/ (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))) (PI))))))))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f)))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* 1/2 (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* f (+ (* 1/2 (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 1/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* f (+ (* 1/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (+ (* 1/6 (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))))) (* 1/2 (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (/ 2 (* f (- (* 1/4 (PI)) (* -1/4 (PI)))))>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt 2>
#<alt (+ 2 (* f (+ (* -1/4 (PI)) (* 1/4 (PI)))))>
#<alt (+ 2 (* f (+ (* -1/4 (PI)) (+ (* 1/16 (* f (pow (PI) 2))) (* 1/4 (PI))))))>
#<alt (+ 2 (* f (+ (* -1/4 (PI)) (+ (* 1/4 (PI)) (* f (+ (* 1/16 (pow (PI) 2)) (* f (+ (* -1/384 (pow (PI) 3)) (* 1/384 (pow (PI) 3))))))))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (* f (- (* 1/4 (PI)) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (+ (* 1/384 (pow (PI) 3)) (* (pow f 2) (- (* 1/122880 (pow (PI) 5)) (* -1/122880 (pow (PI) 5))))) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (+ (* 1/384 (pow (PI) 3)) (* (pow f 2) (- (+ (* 1/122880 (pow (PI) 5)) (* (pow f 2) (- (* 1/82575360 (pow (PI) 7)) (* -1/82575360 (pow (PI) 7))))) (* -1/122880 (pow (PI) 5))))) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))>
#<alt (/ 2 (* f (- (* 1/4 (PI)) (* -1/4 (PI)))))>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))>
#<alt (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))>
#<alt (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))>
#<alt (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))>
#<alt (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))>
#<alt (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))>
#<alt (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))>
#<alt (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* f (- (* 1/4 (PI)) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (+ (* 1/384 (pow (PI) 3)) (* (pow f 2) (- (* 1/122880 (pow (PI) 5)) (* -1/122880 (pow (PI) 5))))) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (+ (* 1/384 (pow (PI) 3)) (* (pow f 2) (- (+ (* 1/122880 (pow (PI) 5)) (* (pow f 2) (- (* 1/82575360 (pow (PI) 7)) (* -1/82575360 (pow (PI) 7))))) (* -1/122880 (pow (PI) 5))))) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>

Calls

36 calls:

Time	Variable		Point	Expression
57.0ms	f	@	-inf	(/ (log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
48.0ms	f	@	inf	(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))
37.0ms	f	@	-inf	(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))
29.0ms	f	@	inf	(/ (log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
4.0ms	f	@	0	(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))

rewrite433.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4240×	`/-lowering-/.f32`
4240×	`/-lowering-/.f64`
4210×	`-lowering-.f32`
4210×	`-lowering-.f64`
1468×	`frac-times`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	202
1	191	98
2	1475	98
0	8243	98

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 957

Calls

Call 1

Inputs
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))
(* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))
(/ 1 (/ (PI) 4))
(log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))
(/ (log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
(log (/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))))
(/ (+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))) (- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4))))
(+ (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))
(- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))
(/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))
(* (/ (PI) 4) f)
(- (exp (* (PI) (/ f 4))) (exp (/ (* (PI) f) -4)))
(* (PI) f)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal -2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)) #s(literal -1/4 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))))) (/.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))) (/.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))))
(neg.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64)))))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (*.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (-.f64 #s(literal 0 binary64) (PI.f64))) #s(literal -1/4 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
(/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64)) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -4 binary64)) (PI.f64))
(/.f64 (*.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (-.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 f #s(literal 4 binary64))))) (exp.f64 (.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)) #s(literal 2 binary64)))))))
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))))
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (log.f64 (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 f #s(literal 4 binary64))))) (exp.f64 (.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)) #s(literal 2 binary64)))))))
(/.f64 (.f64 #s(literal -4 binary64) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)))) (.f64 (PI.f64) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))))
(/.f64 (.f64 #s(literal -4 binary64) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)))) (.f64 (PI.f64) (log.f64 (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 f #s(literal 4 binary64))))) (exp.f64 (.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)) #s(literal 2 binary64)))))))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)))) (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)))) (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 f #s(literal 4 binary64))))) (exp.f64 (.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)) #s(literal 2 binary64)))))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)))) (.f64 #s(literal -1/4 binary64) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)))) (.f64 #s(literal -1/4 binary64) (log.f64 (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 f #s(literal 4 binary64))))) (exp.f64 (.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)) #s(literal 2 binary64)))))))
(/.f64 (.f64 (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
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(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) f))
(.f64 (.f64 f #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 f (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))

simplify232.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

3212×	`-lowering-.f32`
3212×	`-lowering-.f64`
1566×	`+-lowering-+.f64`
1566×	`+-lowering-+.f32`
1430×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	3413
1	749	3003
2	3265	2881
0	8978	2881

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI)))
(- (* -2 (/ (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))) (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))))
(- (* f (- (* -2 (/ (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (PI))) (* 2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))))) (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))))
(- (* f (- (* f (- (* -2/3 (/ (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))) (PI))) (* 2 (/ (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))))) (* 2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))))) (* 4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))))
(* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))
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(* 4 (/ (log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))) (PI)))
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(log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))
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(log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))
(log (/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI))))))))
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eval249.0ms (1.3%)

Compiler: Compiled 56849 to 4396 computations (92.3% saved)

prune175.0ms (0.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	1307	18	1325
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	1309	18	1327

Accuracy

100.0%

Counts

1327 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.8%	(/.f64 (/.f64 (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.0%	(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (.f64 #s(literal 0 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.2%	(/.f64 (-.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))))
	94.9%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.2%	(/.f64 (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	99.3%	(/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
	95.4%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	94.9%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 0 binary64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	94.9%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	99.4%	(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
▶	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (-.f64 #s(literal 0 binary64) (PI.f64)))))
	96.1%	(-.f64 (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)) #s(literal -1/4 binary64)))
	99.2%	(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64))))
▶	99.2%	(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64)))
	94.9%	(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f))))
▶	96.2%	(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
	94.8%	(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))

Compiler

Compiled 868 to 558 computations (35.7% saved)

simplify207.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (PI.f64) #s(literal 4 binary64))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
✓	cost-diff	192	(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (PI.f64))
✓	cost-diff	6464	(pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64))
✓	cost-diff	6592	(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 (PI.f64) #s(literal 4 binary64))
✓	cost-diff	0	(/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
✓	cost-diff	0	(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))
✓	cost-diff	128	(log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))))
✓	cost-diff	128	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	0	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
✓	cost-diff	0	(tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
✓	cost-diff	0	(log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
✓	cost-diff	0	(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))

Rules

2856×	`-lowering-.f32`
2856×	`-lowering-.f64`
1968×	`/-lowering-/.f32`
1968×	`/-lowering-/.f64`
1682×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	325
1	93	320
2	253	313
3	652	313
4	1633	313
5	3765	313
6	7930	313
0	8649	313

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (log (tanh (/ (PI) (/ 4 f)))) (/ (PI) 4))
(log (tanh (/ (PI) (/ 4 f))))
(tanh (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(PI)
(/ 4 f)
4
f
(/ (PI) 4)
(/ (log (/ 2 (* (PI) (* f 1/2)))) (/ (PI) -4))
(log (/ 2 (* (PI) (* f 1/2))))
(/ 2 (* (PI) (* f 1/2)))
2
(* (PI) (* f 1/2))
(PI)
(* f 1/2)
f
1/2
(/ (PI) -4)
-4
(/ 1 (/ (/ (PI) 4) (log (tanh (/ (PI) (/ 4 f))))))
1
(/ (/ (PI) 4) (log (tanh (/ (PI) (/ 4 f)))))
(/ (PI) 4)
(PI)
4
(log (tanh (/ (PI) (/ 4 f))))
(tanh (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(/ 4 f)
f
(* (/ 1 (PI)) (pow (/ 1/4 (log (tanh (/ (PI) (/ 4 f))))) -1))
(/ 1 (PI))
1
(PI)
(pow (/ 1/4 (log (tanh (/ (PI) (/ 4 f))))) -1)
(/ 1/4 (log (tanh (/ (PI) (/ 4 f)))))
1/4
(log (tanh (/ (PI) (/ 4 f))))
(tanh (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(/ 4 f)
4
f
-1
(neg (* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f))))))))
(* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f)))))))
(/ 1 (/ (PI) 4))
1
(/ (PI) 4)
(PI)
4
(- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f))))))
(log (* 2 (cosh (/ (PI) (/ 4 f)))))
(* 2 (cosh (/ (PI) (/ 4 f))))
2
(cosh (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(/ 4 f)
f
(log (* 2 (sinh (/ (PI) (/ 4 f)))))
(* 2 (sinh (/ (PI) (/ 4 f))))
(sinh (/ (PI) (/ 4 f)))

Outputs
(/ (log (tanh (/ (PI) (/ 4 f)))) (/ (PI) 4))
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(log (tanh (/ (PI) (/ 4 f))))
(log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(tanh (/ (PI) (/ 4 f)))
(tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
(/ (PI) (/ 4 f))
(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
(PI)
(PI.f64)
(/ 4 f)
(/.f64 #s(literal 4 binary64) f)
4
#s(literal 4 binary64)
f
(/ (PI) 4)
(/.f64 (PI.f64) #s(literal 4 binary64))
(/ (log (/ 2 (* (PI) (* f 1/2)))) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ 2 (* (PI) (* f 1/2))))
(log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))
(/ 2 (* (PI) (* f 1/2)))
(/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))
2
#s(literal 2 binary64)
(* (PI) (* f 1/2))
(/.f64 (PI.f64) (/.f64 #s(literal 2 binary64) f))
(PI)
(PI.f64)
(* f 1/2)
(*.f64 f #s(literal 1/2 binary64))
f
1/2
#s(literal 1/2 binary64)
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ 1 (/ (/ (PI) 4) (log (tanh (/ (PI) (/ 4 f))))))
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
1
#s(literal 1 binary64)
(/ (/ (PI) 4) (log (tanh (/ (PI) (/ 4 f)))))
(/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(/ (PI) 4)
(/.f64 (PI.f64) #s(literal 4 binary64))
(PI)
(PI.f64)
4
#s(literal 4 binary64)
(log (tanh (/ (PI) (/ 4 f))))
(log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(tanh (/ (PI) (/ 4 f)))
(tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
(/ (PI) (/ 4 f))
(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
(/ 4 f)
(/.f64 #s(literal 4 binary64) f)
f
(* (/ 1 (PI)) (pow (/ 1/4 (log (tanh (/ (PI) (/ 4 f))))) -1))
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/ 1 (PI))
(/.f64 #s(literal 1 binary64) (PI.f64))
1
#s(literal 1 binary64)
(PI)
(PI.f64)
(pow (/ 1/4 (log (tanh (/ (PI) (/ 4 f))))) -1)
(*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(/ 1/4 (log (tanh (/ (PI) (/ 4 f)))))
(/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
1/4
#s(literal 1/4 binary64)
(log (tanh (/ (PI) (/ 4 f))))
(log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(tanh (/ (PI) (/ 4 f)))
(tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
(/ (PI) (/ 4 f))
(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
(/ 4 f)
(/.f64 #s(literal 4 binary64) f)
4
#s(literal 4 binary64)
f
-1
#s(literal -1 binary64)
(neg (* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f))))))))
(/.f64 (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f)))))))
(/.f64 (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/ 1 (/ (PI) 4))
(/.f64 #s(literal 4 binary64) (PI.f64))
1
#s(literal 1 binary64)
(/ (PI) 4)
(/.f64 (PI.f64) #s(literal 4 binary64))
(PI)
(PI.f64)
4
#s(literal 4 binary64)
(- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f))))))
(-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(log (* 2 (cosh (/ (PI) (/ 4 f)))))
(log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(* 2 (cosh (/ (PI) (/ 4 f))))
(*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
2
#s(literal 2 binary64)
(cosh (/ (PI) (/ 4 f)))
(cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
(/ (PI) (/ 4 f))
(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
(/ 4 f)
(/.f64 #s(literal 4 binary64) f)
f
(log (* 2 (sinh (/ (PI) (/ 4 f)))))
(log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(* 2 (sinh (/ (PI) (/ 4 f))))
(*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(sinh (/ (PI) (/ 4 f)))
(sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))

localize381.0ms (2%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
✓	accuracy	99.2%	(log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	accuracy	99.2%	(log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.6%	(/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	accuracy	99.5%	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
✓	accuracy	99.4%	(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64)))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
✓	accuracy	99.6%	(/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	accuracy	99.5%	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))
✓	accuracy	99.4%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	100.0%	(log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
✓	accuracy	99.5%	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
✓	accuracy	99.4%	(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
✓	accuracy	97.7%	(PI.f64)

Results

147.0ms	248×	0	valid
130.0ms	6×	5	exit
25.0ms	1×	5	valid
4.0ms	1×	3	valid

Compiler

Compiled 337 to 38 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 224.0ms

ival-log: 103.0ms (46% of total)

ival-div: 22.0ms (9.8% of total)

ival-cosh: 22.0ms (9.8% of total)

ival-tanh: 17.0ms (7.6% of total)

ival-sinh: 16.0ms (7.1% of total)

ival-mult: 14.0ms (6.2% of total)

ival-sub: 12.0ms (5.4% of total)

ival-pow: 11.0ms (4.9% of total)

backward-pass: 3.0ms (1.3% of total)

const: 1.0ms (0.4% of total)

ival-pi: 1.0ms (0.4% of total)

ival-neg: 1.0ms (0.4% of total)

series309.0ms (1.6%)

Counts

21 → 204

Calls

Call 1

Inputs
#<alt (/ (log (tanh (/ (PI) (/ 4 f)))) (/ (PI) 4))>
#<alt (log (tanh (/ (PI) (/ 4 f))))>
#<alt (tanh (/ (PI) (/ 4 f)))>
#<alt (/ (PI) (/ 4 f))>
#<alt (/ (log (/ 2 (* (PI) (* f 1/2)))) (/ (PI) -4))>
#<alt (log (/ 2 (* (PI) (* f 1/2))))>
#<alt (/ 2 (* (PI) (* f 1/2)))>
#<alt (* (PI) (* f 1/2))>
#<alt (/ 1 (/ (/ (PI) 4) (log (tanh (/ (PI) (/ 4 f))))))>
#<alt (/ (/ (PI) 4) (log (tanh (/ (PI) (/ 4 f)))))>
#<alt (/ (PI) 4)>
#<alt (PI)>
#<alt (* (/ 1 (PI)) (pow (/ 1/4 (log (tanh (/ (PI) (/ 4 f))))) -1))>
#<alt (pow (/ 1/4 (log (tanh (/ (PI) (/ 4 f))))) -1)>
#<alt (/ 1 (PI))>
#<alt (neg (* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f))))))))>
#<alt (* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f)))))))>
#<alt (/ 1 (/ (PI) 4))>
#<alt (/ 1/4 (log (tanh (/ (PI) (/ 4 f)))))>
#<alt (log (* 2 (cosh (/ (PI) (/ 4 f)))))>
#<alt (log (* 2 (sinh (/ (PI) (/ 4 f)))))>

Outputs
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI)))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* f (+ (* 1/2 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI)))))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* f (+ (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* f (+ (* 1/6 (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI))))))) (* 1/2 (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* f (+ (* 1/4 (PI)) (* 1/2 (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))))))>
#<alt (* f (+ (* 1/4 (PI)) (* f (+ (* 1/2 (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (* f (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))))))))>
#<alt (* f (+ (* 1/4 (PI)) (* f (+ (* 1/2 (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (* f (- (+ (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* f (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))))) (* 1/128 (pow (PI) 3))))))))>
#<alt (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 1/4 (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
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#<alt (+ (* f (- (* f (- (* -1 (* f (+ (* -2 (/ (* (+ (* -1 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (pow (PI) 2) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/8 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (* (PI) (+ (log f) (log (* 1/4 (PI))))))) (+ (* -1/4 (/ (* (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/24 (/ (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))))))) (+ (* -1 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (pow (PI) 2) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/8 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (* 1/2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (* 1/4 (/ 1 (+ (log f) (log (* 1/4 (PI)))))))>
#<alt (/ 1/4 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1/4 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1/4 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1/4 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1/4 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1/4 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1/4 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1/4 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (log 2)>
#<alt (+ (log 2) (* 1/32 (* (pow f 2) (pow (PI) 2))))>
#<alt (+ (log 2) (* (pow f 2) (+ (* -1/2 (* f (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/32 (pow (PI) 2)))))>
#<alt (+ (log 2) (* (pow f 2) (+ (* 1/32 (pow (PI) 2)) (* f (+ (* -1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3)))) (* 1/24 (* f (+ (* -12 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/1536 (pow (PI) 4))))) (* -3/256 (pow (PI) 4))))))))))>
#<alt (log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (+ (log f) (log (* 1/2 (PI))))>
#<alt (+ (log f) (+ (log (* 1/2 (PI))) (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI)))))>
#<alt (+ (log f) (+ (log (* 1/2 (PI))) (* f (+ (* 1/2 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 4 (/ (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3)))) (PI)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI)))))))>
#<alt (+ (log f) (+ (log (* 1/2 (PI))) (* f (+ (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* f (+ (* 1/6 (* f (+ (* -24 (/ (* (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))) (+ (* 12 (/ (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4))))) (PI))) (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))))))) (* 1/2 (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 4 (/ (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3)))) (PI)))))))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>

Calls

51 calls:

Time	Variable		Point	Expression
111.0ms	f	@	inf	(neg (* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f))))))))
42.0ms	f	@	-inf	(neg (* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f))))))))
40.0ms	f	@	-inf	(/ (log (tanh (/ (PI) (/ 4 f)))) (/ (PI) 4))
25.0ms	f	@	inf	(/ (log (tanh (/ (PI) (/ 4 f)))) (/ (PI) 4))
21.0ms	f	@	-inf	(/ (log (/ 2 (* (PI) (* f 1/2)))) (/ (PI) -4))

rewrite466.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3490×	`/-lowering-/.f32`
3490×	`/-lowering-/.f64`
3468×	`-lowering-.f32`
3468×	`-lowering-.f64`
1562×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	176
1	210	157
2	1493	155
0	8271	155

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1291

Calls

Call 1

Inputs
(/ (log (tanh (/ (PI) (/ 4 f)))) (/ (PI) 4))
(log (tanh (/ (PI) (/ 4 f))))
(tanh (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(/ (log (/ 2 (* (PI) (* f 1/2)))) (/ (PI) -4))
(log (/ 2 (* (PI) (* f 1/2))))
(/ 2 (* (PI) (* f 1/2)))
(* (PI) (* f 1/2))
(/ 1 (/ (/ (PI) 4) (log (tanh (/ (PI) (/ 4 f))))))
(/ (/ (PI) 4) (log (tanh (/ (PI) (/ 4 f)))))
(/ (PI) 4)
(PI)
(* (/ 1 (PI)) (pow (/ 1/4 (log (tanh (/ (PI) (/ 4 f))))) -1))
(pow (/ 1/4 (log (tanh (/ (PI) (/ 4 f))))) -1)
(/ 1 (PI))
(neg (* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f))))))))
(* (/ 1 (/ (PI) 4)) (- (log (* 2 (cosh (/ (PI) (/ 4 f))))) (log (* 2 (sinh (/ (PI) (/ 4 f)))))))
(/ 1 (/ (PI) 4))
(/ 1/4 (log (tanh (/ (PI) (/ 4 f)))))
(log (* 2 (cosh (/ (PI) (/ 4 f)))))
(log (* 2 (sinh (/ (PI) (/ 4 f)))))

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(+.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (neg.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
(+.f64 (neg.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (neg.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 #s(literal -4 binary64) (PI.f64)))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (.f64 #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64)))) (.f64 #s(literal 1 binary64) (neg.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 #s(literal -4 binary64) (PI.f64))))))
(+.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (.f64 #s(literal -1 binary64) (neg.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))))
(+.f64 (.f64 #s(literal -1 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))) (.f64 #s(literal -1 binary64) (neg.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 #s(literal 4 binary64) (PI.f64))))))
(+.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(+.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (PI.f64)) #s(literal -1 binary64)) (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 1/4 binary64)))))
(exp.f64 (+.f64 (-.f64 #s(literal 0 binary64) (log.f64 (PI.f64))) (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 1/4 binary64)))))
(exp.f64 (+.f64 (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 1/4 binary64))) (*.f64 (log.f64 (PI.f64)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 (PI.f64)))))
(exp.f64 (-.f64 (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 1/4 binary64))) (log.f64 (PI.f64))))
(-.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 (log.f64 (expm1.f64 (.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log1p.f64 (exp.f64 (.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log1p.f64 (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64))))
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(-.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))
(-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 3 binary64))) (exp.f64 (.f64 (.f64 f (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64))))) (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 2 binary64))) (+.f64 (exp.f64 (+.f64 (.f64 f (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 f (/.f64 (PI.f64) #s(literal -4 binary64))))) #s(literal -1 binary64)))))
(-.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (log.f64 #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (/.f64 (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
(/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
(/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))))
(/.f64 (neg.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (neg.f64 (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (+.f64 (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (log.f64 #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (log.f64 #s(literal 2 binary64))))
(.f64 #s(literal 1 binary64) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 1 binary64))
(.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))))
(.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(+.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (log.f64 #s(literal 2 binary64)))
(+.f64 (neg.f64 (log.f64 #s(literal 1/2 binary64))) (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(-.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(-.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 3 binary64))) (exp.f64 (.f64 (.f64 f (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64))))) (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 2 binary64))) (+.f64 (exp.f64 (+.f64 (.f64 f (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 f (/.f64 (PI.f64) #s(literal -4 binary64))))) #s(literal 1 binary64)))))
(-.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (log.f64 #s(literal 2 binary64)))
(-.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (/.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
(/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
(/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))))
(/.f64 (neg.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (neg.f64 (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (+.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (log.f64 #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (log.f64 #s(literal 2 binary64))))
(.f64 #s(literal 1 binary64) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))))
(.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))

simplify311.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

4274×	`-lowering-.f32`
4274×	`-lowering-.f64`
1972×	`+-lowering-+.f64`
1972×	`+-lowering-+.f32`
1964×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	380	6838
1	1348	5777
2	6370	5774
0	8273	5774

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(+ (log f) (log (* 1/4 (PI))))
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Outputs
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(log (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(+ (log f) (log (* 1/2 (PI))))
(+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(+ (log f) (+ (log (* 1/2 (PI))) (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI)))))
(+.f64 (log.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (log.f64 f) (/.f64 (.f64 f #s(literal 0 binary64)) (PI.f64))))
(+ (log f) (+ (log (* 1/2 (PI))) (* f (+ (* 1/2 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 4 (/ (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3)))) (PI)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI)))))))
(+.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (.f64 f (+.f64 (/.f64 #s(literal 0 binary64) (PI.f64)) (.f64 f (+.f64 (/.f64 #s(literal 0 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 (.f64 (PI.f64) (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64)) #s(literal -1/4 binary64))) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/384 binary64)))) (PI.f64))))))))
(+ (log f) (+ (log (* 1/2 (PI))) (* f (+ (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* f (+ (* 1/6 (* f (+ (* -24 (/ (* (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))) (+ (* 12 (/ (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4))))) (PI))) (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))))))) (* 1/2 (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 4 (/ (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3)))) (PI)))))))))))
(+.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (.f64 f (+.f64 (/.f64 #s(literal 0 binary64) (PI.f64)) (.f64 f (+.f64 (.f64 (+.f64 (/.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (PI.f64) (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64)) #s(literal -1/4 binary64))) (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/192 binary64))) (.f64 (PI.f64) #s(literal -1/4 binary64))) (+.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64)) #s(literal -1/32 binary64))) (.f64 (pow.f64 (PI.f64) #s(literal 4 binary64)) #s(literal -1/3072 binary64)))) #s(literal 12 binary64)) (PI.f64)) (+.f64 (/.f64 #s(literal 0 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (.f64 (+.f64 (.f64 (PI.f64) (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64)) #s(literal -1/4 binary64))) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/384 binary64)))) (/.f64 #s(literal 0 binary64) (.f64 (PI.f64) (PI.f64)))))) (.f64 f #s(literal 1/6 binary64))) (+.f64 (/.f64 #s(literal 0 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 (.f64 (PI.f64) (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64)) #s(literal -1/4 binary64))) (.f64 (PI.f64) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -1/384 binary64)))) (PI.f64)))))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))

eval424.0ms (2.2%)

Compiler: Compiled 78883 to 7287 computations (90.8% saved)

prune310.0ms (1.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	2733	16	2749
Fresh	12	1	13
Picked	5	0	5
Done	0	0	0
Total	2750	17	2767

Accuracy

100.0%

Counts

2767 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
	94.8%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	94.8%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	94.7%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	10.1%	(/.f64 (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))) (log1p.f64 (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
▶	95.4%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	94.9%	(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	94.5%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
	99.0%	(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal 4 binary64)))
▶	99.3%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
▶	94.9%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64))))
	99.3%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)))
	94.8%	(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
▶	94.7%	(-.f64 (/.f64 (/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64)) #s(literal -1/4 binary64)))
▶	94.8%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
	94.9%	(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))

Compiler

Compiled 540 to 416 computations (23% saved)

simplify195.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64))
✓	cost-diff	0	(/.f64 (/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64)) #s(literal -1/4 binary64))
✓	cost-diff	0	(-.f64 (/.f64 (/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64)) #s(literal -1/4 binary64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 (PI.f64) #s(literal 4 binary64))
✓	cost-diff	0	(/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))))
✓	cost-diff	1024	(+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64))))))))
✓	cost-diff	1024	(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)
✓	cost-diff	1024	(log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f))
✓	cost-diff	1024	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	0	(log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 #s(literal -4 binary64) (PI.f64))
✓	cost-diff	0	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
✓	cost-diff	0	(log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))

Rules

4104×	`-lowering-.f32`
4104×	`-lowering-.f64`
2048×	`/-lowering-/.f32`
2048×	`/-lowering-/.f64`
1720×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	413
1	128	365
2	341	348
3	998	334
4	2948	290
5	5901	290
6	7283	290
0	8017	290

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 4 (/ (PI) (log (tanh (/ (PI) (/ 4 f))))))
4
(/ (PI) (log (tanh (/ (PI) (/ 4 f)))))
(PI)
(log (tanh (/ (PI) (/ 4 f))))
(tanh (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(/ 4 f)
f
(* (/ -4 (PI)) (log (/ (/ 4 f) (PI))))
(/ -4 (PI))
-4
(PI)
(log (/ (/ 4 f) (PI)))
(/ (/ 4 f) (PI))
(/ 4 f)
4
f
(/ (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f)) (/ (PI) -4))
(log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f))
(/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f)
(+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))))))
(/ 2 (* (PI) 1/2))
2
(* (PI) 1/2)
(PI)
1/2
(* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))
f
(* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))))
(+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))
(* 1/16 (* (PI) 2))
1/16
(* (PI) 2)
(* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))
-2
(* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))
(* (PI) (* (PI) 2))
(/ 1/96 (PI))
1/96
(/ (PI) -4)
-4
(/ 1 (/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI))))))
1
(/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI)))))
(/ (PI) 4)
(PI)
4
(+ (log f) (log (* 1/4 (PI))))
(log f)
f
(log (* 1/4 (PI)))
(* 1/4 (PI))
1/4
(- (/ (/ (log 2) (PI)) -1/4) (/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4))
(/ (/ (log 2) (PI)) -1/4)
(/ (log 2) (PI))
(log 2)
2
(PI)
-1/4
(/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4)
(/ (log (* (PI) (* f 1/2))) (PI))
(log (* (PI) (* f 1/2)))
(* (PI) (* f 1/2))
(* f 1/2)
f
1/2

Outputs
(/ 4 (/ (PI) (log (tanh (/ (PI) (/ 4 f))))))
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
4
#s(literal 4 binary64)
(/ (PI) (log (tanh (/ (PI) (/ 4 f)))))
(/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(PI)
(PI.f64)
(log (tanh (/ (PI) (/ 4 f))))
(log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(tanh (/ (PI) (/ 4 f)))
(tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
(/ (PI) (/ 4 f))
(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
(/ 4 f)
(/.f64 #s(literal 4 binary64) f)
f
(* (/ -4 (PI)) (log (/ (/ 4 f) (PI))))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))
(/ -4 (PI))
(/.f64 #s(literal -4 binary64) (PI.f64))
-4
#s(literal -4 binary64)
(PI)
(PI.f64)
(log (/ (/ 4 f) (PI)))
(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)))
(/ (/ 4 f) (PI))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 f)
(/.f64 #s(literal 4 binary64) f)
4
#s(literal 4 binary64)
f
(/ (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f)) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f))
(log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) (*.f64 f f)))) f))
(/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f)
(/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) (*.f64 f f)))) f)
(+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))))))
(+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) (*.f64 f f))))
(/ 2 (* (PI) 1/2))
(/.f64 #s(literal 4 binary64) (PI.f64))
2
#s(literal 2 binary64)
(* (PI) 1/2)
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(PI)
(PI.f64)
1/2
#s(literal 1/2 binary64)
(* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))
(.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) (*.f64 f f)))
f
(* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))))
(.f64 (.f64 (PI.f64) f) #s(literal 1/12 binary64))
(+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))
(*.f64 (PI.f64) #s(literal 1/12 binary64))
(* 1/16 (* (PI) 2))
(*.f64 (PI.f64) #s(literal 1/8 binary64))
1/16
#s(literal 1/16 binary64)
(* (PI) 2)
(*.f64 (PI.f64) #s(literal 2 binary64))
(* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))
(*.f64 (PI.f64) #s(literal -1/24 binary64))
-2
#s(literal -2 binary64)
(* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))
(*.f64 (PI.f64) #s(literal 1/48 binary64))
(* (PI) (* (PI) 2))
(.f64 (PI.f64) (.f64 (PI.f64) #s(literal 2 binary64)))
(/ 1/96 (PI))
(/.f64 #s(literal 1/96 binary64) (PI.f64))
1/96
#s(literal 1/96 binary64)
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ 1 (/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI))))))
(/.f64 (+.f64 (log.f64 f) (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
1
#s(literal 1 binary64)
(/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI)))))
(/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (+.f64 (log.f64 f) (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64)))))
(/ (PI) 4)
(/.f64 (PI.f64) #s(literal 4 binary64))
(PI)
(PI.f64)
4
#s(literal 4 binary64)
(+ (log f) (log (* 1/4 (PI))))
(+.f64 (log.f64 f) (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))))
(log f)
(log.f64 f)
f
(log (* 1/4 (PI)))
(log.f64 (/.f64 (PI.f64) #s(literal 4 binary64)))
(* 1/4 (PI))
(/.f64 (PI.f64) #s(literal 4 binary64))
1/4
#s(literal 1/4 binary64)
(- (/ (/ (log 2) (PI)) -1/4) (/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4))
(+.f64 (/.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(/ (/ (log 2) (PI)) -1/4)
(/.f64 (log.f64 #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/ (log 2) (PI))
(/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64))
(log 2)
(log.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(PI)
(PI.f64)
-1/4
#s(literal -1/4 binary64)
(/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4)
(/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/ (log (* (PI) (* f 1/2))) (PI))
(/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64))
(log (* (PI) (* f 1/2)))
(log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))
(* (PI) (* f 1/2))
(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
(* f 1/2)
(*.f64 f #s(literal 1/2 binary64))
f
1/2
#s(literal 1/2 binary64)

localize316.0ms (1.6%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64))
✓	accuracy	99.5%	(-.f64 (/.f64 (/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64)) #s(literal -1/4 binary64)))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.7%	(+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))
✓	accuracy	99.6%	(/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	97.6%	(log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))
✓	accuracy	99.0%	(.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64))))))
✓	accuracy	98.5%	(/.f64 #s(literal 1/96 binary64) (PI.f64))
✓	accuracy	98.5%	(+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	100.0%	(log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))
✓	accuracy	99.5%	(/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))
✓	accuracy	99.4%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.7%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
✓	accuracy	99.6%	(/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	accuracy	99.5%	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
✓	accuracy	97.7%	(PI.f64)

Results

143.0ms	248×	0	valid
65.0ms	6×	5	exit
9.0ms	1×	5	valid
3.0ms	1×	3	valid

Compiler

Compiled 423 to 55 computations (87% saved)

Precisions

Click to see histograms. Total time spent on operations: 158.0ms

ival-log: 64.0ms (40.5% of total)

ival-div: 35.0ms (22.2% of total)

ival-mult: 23.0ms (14.6% of total)

ival-tanh: 19.0ms (12% of total)

...c/correct-round.rkt:119:19: 4.0ms (2.5% of total)

backward-pass: 4.0ms (2.5% of total)

ival-add: 4.0ms (2.5% of total)

const: 1.0ms (0.6% of total)

ival-pi: 1.0ms (0.6% of total)

ival-sub: 1.0ms (0.6% of total)

series264.0ms (1.4%)

Counts

27 → 216

Calls

Call 1

Inputs
#<alt (/ 4 (/ (PI) (log (tanh (/ (PI) (/ 4 f))))))>
#<alt (/ (PI) (log (tanh (/ (PI) (/ 4 f)))))>
#<alt (PI)>
#<alt (log (tanh (/ (PI) (/ 4 f))))>
#<alt (* (/ -4 (PI)) (log (/ (/ 4 f) (PI))))>
#<alt (/ -4 (PI))>
#<alt (log (/ (/ 4 f) (PI)))>
#<alt (/ (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f)) (/ (PI) -4))>
#<alt (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f))>
#<alt (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f)>
#<alt (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))))))>
#<alt (/ 1 (/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI)))))>
#<alt (/ (PI) 4)>
#<alt (- (/ (/ (log 2) (PI)) -1/4) (/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4))>
#<alt (/ (/ (log 2) (PI)) -1/4)>
#<alt (/ (log 2) (PI))>
#<alt (log 2)>
#<alt (/ (PI) (/ 4 f))>
#<alt (/ (/ 4 f) (PI))>
#<alt (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))>
#<alt (/ 1/96 (PI))>
#<alt (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))))>
#<alt (log (* 1/4 (PI)))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (/ (log (* (PI) (* f 1/2))) (PI))>
#<alt (* (PI) (* f 1/2))>

Outputs
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (/ (PI) (+ (log f) (log (* 1/4 (PI)))))>
#<alt (+ (* -2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))) (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (+ (* f (- (* -1 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (* (PI) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))))) (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (+ (* f (- (* f (- (* -1 (* f (+ (* -2 (/ (* (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (* (PI) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (* (PI) (+ (log f) (log (* 1/4 (PI))))))) (+ (* -1 (/ (* (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (+ (log f) (log (* 1/4 (PI)))) 3))) (* 1/6 (/ (* (PI) (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))))))) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (* (PI) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))))) (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI)))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* f (+ (* 1/2 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI)))))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* f (+ (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* f (+ (* 1/6 (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI))))))) (* 1/2 (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* -1 (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))))>
#<alt (+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 1/8 (* (pow f 2) (* (PI) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2)))))))>
#<alt (+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* (pow f 2) (+ (* -1/48 (* (pow f 2) (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 3)))) (* 1/8 (* (PI) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2))))))))>
#<alt (* -4 (/ (+ (log (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* -1 (log (/ 1 f)))) (PI)))>
#<alt (- (* -4 (/ (+ (log (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* -1 (log (/ 1 f)))) (PI))) (* 16 (/ 1 (* (pow f 2) (* (pow (PI) 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))))))>
#<alt (- (+ (* -4 (/ (+ (log (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* -1 (log (/ 1 f)))) (PI))) (/ 32 (* (pow f 4) (* (pow (PI) 3) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2))))) (/ 16 (* (pow f 2) (* (pow (PI) 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))>
#<alt (- (+ (* -4 (/ (+ (log (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* -1 (log (/ 1 f)))) (PI))) (* 32 (/ 1 (* (pow f 4) (* (pow (PI) 3) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2)))))) (+ (* 256/3 (/ 1 (* (pow f 6) (* (pow (PI) 4) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 3))))) (/ 16 (* (pow f 2) (* (pow (PI) 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))))))>
#<alt (* -4 (/ (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (* -1 (log (/ -1 f)))) (PI)))>
#<alt (- (* -4 (/ (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (* -1 (log (/ -1 f)))) (PI))) (* 16 (/ 1 (* (pow f 2) (* (pow (PI) 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))))))>
#<alt (- (+ (* -4 (/ (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (* -1 (log (/ -1 f)))) (PI))) (/ 32 (* (pow f 4) (* (pow (PI) 3) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2))))) (/ 16 (* (pow f 2) (* (pow (PI) 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))>
#<alt (- (+ (* -4 (/ (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (* -1 (log (/ -1 f)))) (PI))) (* 32 (/ 1 (* (pow f 4) (* (pow (PI) 3) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2)))))) (+ (* 256/3 (/ 1 (* (pow f 6) (* (pow (PI) 4) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 3))))) (/ 16 (* (pow f 2) (* (pow (PI) 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))))))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* 1/4 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI))))))))>
#<alt (+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* (pow f 2) (+ (* -1/32 (* (pow f 2) (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2)))) (* 1/4 (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))))>
#<alt (+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* (pow f 2) (+ (* 1/4 (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI))))) (* (pow f 2) (+ (* -1/32 (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2))) (* 1/192 (* (pow f 2) (* (pow (PI) 3) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 3))))))))))>
#<alt (+ (log (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* -1 (log (/ 1 f))))>
#<alt (+ (log (+ (* -1/24 (PI)) (* 1/8 (PI)))) (+ (* -1 (log (/ 1 f))) (* 4 (/ 1 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))))>
#<alt (- (+ (log (+ (* -1/24 (PI)) (* 1/8 (PI)))) (+ (* -1 (log (/ 1 f))) (/ 4 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))) (/ 8 (* (pow f 4) (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2)))))>
#<alt (- (+ (log (+ (* -1/24 (PI)) (* 1/8 (PI)))) (+ (* -1 (log (/ 1 f))) (+ (* 64/3 (/ 1 (* (pow f 6) (* (pow (PI) 3) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 3))))) (/ 4 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI))))))))) (* 8 (/ 1 (* (pow f 4) (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2))))))>
#<alt (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (* -1 (log (/ -1 f))))>
#<alt (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (+ (* -1 (log (/ -1 f))) (* 4 (/ 1 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))))>
#<alt (- (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (+ (* -1 (log (/ -1 f))) (/ 4 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))) (/ 8 (* (pow f 4) (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2)))))>
#<alt (- (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (+ (* -1 (log (/ -1 f))) (+ (* 64/3 (/ 1 (* (pow f 6) (* (pow (PI) 3) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 3))))) (/ 4 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI))))))))) (* 8 (/ 1 (* (pow f 4) (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2))))))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI)))) f)>
#<alt (/ (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI)))) f)>
#<alt (/ (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI)))) f)>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* f (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* f (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (/ 4 (PI))>
#<alt (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI))))>
#<alt (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI))))>
#<alt (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (* 4 (/ (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f)))) (PI)))>
#<alt (* 4 (/ (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f)))) (PI)))>
#<alt (* 4 (/ (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f)))) (PI)))>
#<alt (* 4 (/ (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f)))) (PI)))>
#<alt (* 4 (/ (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f))))) (PI)))>
#<alt (* 4 (/ (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f))))) (PI)))>
#<alt (* 4 (/ (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f))))) (PI)))>
#<alt (* 4 (/ (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f))))) (PI)))>
#<alt (* 1/4 (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (* 1/4 (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (* 1/4 (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (* 1/4 (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (* 1/4 (/ (PI) (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))))>
#<alt (* 1/4 (/ (PI) (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))))>
#<alt (* 1/4 (/ (PI) (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))))>
#<alt (* 1/4 (/ (PI) (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))))>
#<alt (* 1/4 (/ (PI) (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))))>
#<alt (* 1/4 (/ (PI) (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))))>
#<alt (* 1/4 (/ (PI) (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))))>
#<alt (* 1/4 (/ (PI) (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log f) (log (* 1/2 (PI)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log f) (log (* 1/2 (PI)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log f) (log (* 1/2 (PI)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log f) (log (* 1/2 (PI)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))))>
#<alt (- (* -4 (/ (log 2) (PI))) (* -4 (/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))>
#<alt (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))>
#<alt (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))>
#<alt (+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))>
#<alt (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))>
#<alt (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))>
#<alt (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))>
#<alt (+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))>
#<alt (/ (+ (log f) (log (* 1/2 (PI)))) (PI))>
#<alt (/ (+ (log f) (log (* 1/2 (PI)))) (PI))>
#<alt (/ (+ (log f) (log (* 1/2 (PI)))) (PI))>
#<alt (/ (+ (log f) (log (* 1/2 (PI)))) (PI))>
#<alt (/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))>
#<alt (/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))>
#<alt (/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))>
#<alt (/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))>
#<alt (/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))>
#<alt (/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))>
#<alt (/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))>
#<alt (/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>
#<alt (* 1/2 (* f (PI)))>

Calls

54 calls:

Time	Variable		Point	Expression
150.0ms	f	@	-inf	(- (/ (/ (log 2) (PI)) -1/4) (/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4))
33.0ms	f	@	0	(- (/ (/ (log 2) (PI)) -1/4) (/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4))
30.0ms	f	@	0	(/ 1 (/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI))))))
14.0ms	f	@	-inf	(/ 1 (/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI))))))
10.0ms	f	@	inf	(/ 1 (/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI))))))

rewrite427.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3760×	`/-lowering-/.f32`
3760×	`/-lowering-/.f64`
3510×	`-lowering-.f32`
3510×	`-lowering-.f64`
2284×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	283
1	314	245
2	3012	244
0	8960	244

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 1082

Calls

Call 1

Inputs
(/ 4 (/ (PI) (log (tanh (/ (PI) (/ 4 f))))))
(/ (PI) (log (tanh (/ (PI) (/ 4 f)))))
(PI)
(log (tanh (/ (PI) (/ 4 f))))
(* (/ -4 (PI)) (log (/ (/ 4 f) (PI))))
(/ -4 (PI))
(log (/ (/ 4 f) (PI)))
(/ (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f)) (/ (PI) -4))
(log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f))
(/ (+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))))) f)
(+ (/ 2 (* (PI) 1/2)) (* f (* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))))))
(/ 1 (/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI))))))
(/ (/ (PI) 4) (+ (log f) (log (* 1/4 (PI)))))
(/ (PI) 4)
(- (/ (/ (log 2) (PI)) -1/4) (/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4))
(/ (/ (log 2) (PI)) -1/4)
(/ (log 2) (PI))
(log 2)
(/ (PI) (/ 4 f))
(/ (/ 4 f) (PI))
(+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI)))))
(/ 1/96 (PI))
(* f (+ (* 1/16 (* (PI) 2)) (* -2 (* (* (PI) (* (PI) 2)) (/ 1/96 (PI))))))
(log (* 1/4 (PI)))
(+ (log f) (log (* 1/4 (PI))))
(/ (log (* (PI) (* f 1/2))) (PI))
(* (PI) (* f 1/2))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (PI.f64) (.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 #s(literal -4 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (neg.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (PI.f64) (*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (PI.f64) (*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))
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(+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))) (log.f64 (*.f64 (cbrt.f64 (PI.f64)) (/.f64 f #s(literal 4 binary64)))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))) (log.f64 (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) f))))
(+.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (log.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 f #s(literal 4 binary64)))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (log.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) f))))
(+.f64 (log.f64 (*.f64 (PI.f64) f)) (log.f64 #s(literal 1/4 binary64)))
(+.f64 (log.f64 (-.f64 #s(literal 0 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -4 binary64) f))))
(+.f64 (log.f64 (/.f64 f #s(literal 4 binary64))) (log.f64 (PI.f64)))
(+.f64 (log.f64 (/.f64 (PI.f64) #s(literal -4 binary64))) (log.f64 (-.f64 #s(literal 0 binary64) f)))
(+.f64 (log.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64))) (log.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) f))))
(+.f64 (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -4 binary64) f))) (log.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(+.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 4 binary64))) (log.f64 (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) f))))
(+.f64 (log.f64 (/.f64 (PI.f64) #s(literal 1 binary64))) (log.f64 (/.f64 f #s(literal 4 binary64))))
(-.f64 (log.f64 f) (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))))
(-.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 f)))
(-.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) f)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)) #s(literal 1 binary64))))
(-.f64 (log.f64 (*.f64 (PI.f64) f)) (log.f64 #s(literal 4 binary64)))
(-.f64 (log.f64 (-.f64 #s(literal 0 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -4 binary64) f)))
(-.f64 (log.f64 (/.f64 f #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 (PI.f64))))
(-.f64 (/.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))) (/.f64 (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 2 binary64)) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)))))
(-.f64 (log.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64)))) (log.f64 (/.f64 #s(literal 4 binary64) f)))
(-.f64 (log.f64 (*.f64 f #s(literal 1 binary64))) (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))))
(-.f64 (log.f64 (*.f64 f (-.f64 #s(literal 0 binary64) (PI.f64)))) (log.f64 #s(literal -4 binary64)))
(-.f64 (log.f64 (*.f64 #s(literal 1 binary64) f)) (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))))
(-.f64 (log.f64 (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) f)) (log.f64 #s(literal -4 binary64)))
(neg.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))))
(neg.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))) (*.f64 (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))) (*.f64 (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))))))
(/.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))
(/.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 f) (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64)))))))
(/.f64 (*.f64 (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 f) (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))))))))
(/.f64 (neg.f64 (*.f64 (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))))) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 2 binary64)) (pow.f64 (log.f64 f) #s(literal 2 binary64))) (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))))) (neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 2 binary64)) (pow.f64 (log.f64 f) #s(literal 2 binary64)))) (neg.f64 (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))
(pow.f64 (/.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))) (*.f64 (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))))) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))
(.f64 (+.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (pow.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))
(.f64 (.f64 (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))))))
(/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) #s(literal 1 binary64))))
(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (PI.f64))
(/.f64 (neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (PI.f64))
(/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64)))))
(/.f64 (neg.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (neg.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (neg.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (neg.f64 (cbrt.f64 (PI.f64))))
(/.f64 (neg.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))))
(pow.f64 (/.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))) (PI.f64)))
(.f64 (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))))
(.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (log.f64 (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f))
(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f)
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64))))
(.f64 (.f64 f #s(literal 1/2 binary64)) (PI.f64))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 f #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 f #s(literal 1/2 binary64))))
(.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))
(.f64 (.f64 (*.f64 f #s(literal 1/2 binary64)) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 f #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 f #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))

simplify307.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

4244×	`-lowering-.f32`
4244×	`-lowering-.f64`
1698×	`+-lowering-+.f64`
1698×	`+-lowering-+.f32`
1690×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	4118
1	1248	3674
2	5396	3658
0	8308	3658

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(* f (+ (* -1/24 (PI)) (* 1/8 (PI))))
(* f (+ (* -1/24 (PI)) (* 1/8 (PI))))
(+ (log f) (log (* 1/4 (PI))))
(+ (log f) (log (* 1/4 (PI))))
(+ (log f) (log (* 1/4 (PI))))
(+ (log f) (log (* 1/4 (PI))))
(+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))
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(+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))
(+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))
(+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))
(+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))
(+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))
(+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))
(/ (+ (log f) (log (* 1/2 (PI)))) (PI))
(/ (+ (log f) (log (* 1/2 (PI)))) (PI))
(/ (+ (log f) (log (* 1/2 (PI)))) (PI))
(/ (+ (log f) (log (* 1/2 (PI)))) (PI))
(/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))
(/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))
(/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))
(/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))
(/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))
(/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))
(/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))
(/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))
(* 1/2 (* f (PI)))
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(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))
(* 1/2 (* f (PI)))

Outputs
(* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))
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(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(/ (PI) (+ (log f) (log (* 1/4 (PI)))))
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(+ (log f) (log (* 1/4 (PI))))
(+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))
(+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))
(+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))
(+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))
(+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))
(+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))
(+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))
(+ (log (* 1/4 (PI))) (* -1 (log (/ 1 f))))
(+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))
(+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))
(-.f64 (+.f64 (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))) (log.f64 #s(literal -1 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f)))
(+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))
(-.f64 (+.f64 (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))) (log.f64 #s(literal -1 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f)))
(+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))
(-.f64 (+.f64 (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))) (log.f64 #s(literal -1 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f)))
(+ (log -1) (+ (log (* 1/4 (PI))) (* -1 (log (/ -1 f)))))
(-.f64 (+.f64 (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))) (log.f64 #s(literal -1 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f)))
(/ (+ (log f) (log (* 1/2 (PI)))) (PI))
(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (PI.f64))
(/ (+ (log f) (log (* 1/2 (PI)))) (PI))
(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (PI.f64))
(/ (+ (log f) (log (* 1/2 (PI)))) (PI))
(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (PI.f64))
(/ (+ (log f) (log (* 1/2 (PI)))) (PI))
(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (PI.f64))
(/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))
(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (PI.f64))
(/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))
(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (PI.f64))
(/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))
(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (PI.f64))
(/ (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f)))) (PI))
(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (PI.f64))
(/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))
(/.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (PI.f64))
(/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))
(/.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (PI.f64))
(/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))
(/.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (PI.f64))
(/ (+ (log (* -1/2 (PI))) (* -1 (log (/ -1 f)))) (PI))
(/.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (PI.f64))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 1/2 (* f (PI)))
(.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))

eval536.0ms (2.8%)

Compiler: Compiled 47991 to 7276 computations (84.8% saved)

prune255.0ms (1.3%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	1873	13	1886
Fresh	7	5	12
Picked	2	3	5
Done	0	0	0
Total	1882	21	1903

Accuracy

100.0%

Counts

1903 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.9%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) #s(literal -1/4 binary64)) (PI.f64))
▶	94.7%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
	94.8%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	94.8%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	94.7%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	95.4%	(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.4%	(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.4%	(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
	1.6%	(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	99.0%	(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal 4 binary64)))
	10.1%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f)))))) (log1p.f64 (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))))))
	94.9%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))))
✓	99.3%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
▶	99.3%	(/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))))
	94.8%	(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
▶	94.8%	(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
✓	94.7%	(-.f64 (/.f64 (/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64)) #s(literal -1/4 binary64)))
	94.8%	(+.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64)))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 f)))
	94.4%	(.f64 (/.f64 #s(literal -4 binary64) (cbrt.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
	94.9%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
✓	94.8%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))

Compiler

Compiled 713 to 478 computations (33% saved)

simplify437.0ms (2.3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f)))
✓	cost-diff	0	(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	2048	(/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f))))
✓	cost-diff	2176	(/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f)))) f)
✓	cost-diff	2176	(log.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f)))) f))
✓	cost-diff	2176	(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (PI.f64))
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	cost-diff	0	(log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
✓	cost-diff	0	(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
✓	cost-diff	0	(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	cost-diff	0	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)))
✓	cost-diff	128	(/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))))

Rules

3696×	`-lowering-.f32`
3696×	`-lowering-.f64`
1324×	`fma-lowering-fma.f32`
1324×	`fma-lowering-fma.f64`
1282×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	608
1	132	560
2	389	530
3	1544	381
4	6582	381
0	8047	381

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 4 (/ 1 (/ (log (tanh (/ f (/ 4 (PI))))) (PI))))
4
(/ 1 (/ (log (tanh (/ f (/ 4 (PI))))) (PI)))
1
(/ (log (tanh (/ f (/ 4 (PI))))) (PI))
(log (tanh (/ f (/ 4 (PI)))))
(tanh (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ 4 (PI))
(PI)
(/ -4 (/ (PI) (log (/ (/ 4 f) (PI)))))
-4
(/ (PI) (log (/ (/ 4 f) (PI))))
(PI)
(log (/ (/ 4 f) (PI)))
(/ (/ 4 f) (PI))
(/ 4 f)
4
f
(/ (/ 4 (PI)) (/ 1 (log (/ f (/ 4 (PI))))))
(/ 4 (PI))
4
(PI)
(/ 1 (log (/ f (/ 4 (PI)))))
1
(log (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ (log (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f)) (/ (PI) -4))
(log (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f))
(/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f)
(/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f))))
(- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f))))
(/ (/ -4 (PI)) (/ (PI) -4))
(/ -4 (PI))
-4
(PI)
(/ (PI) -4)
(* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))
(* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f))
(+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI)))
(* (PI) 1/8)
1/8
(/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))
(* -2 (* (* (PI) (PI)) 1/48))
-2
(* (* (PI) (PI)) 1/48)
(* (PI) (PI))
1/48
(* f f)
f
(- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))
(/ 4 (PI))
4
(/ (- (log (/ 2 (* (PI) f))) (log 1/2)) (/ (PI) -4))
(- (log (/ 2 (* (PI) f))) (log 1/2))
(log (/ 2 (* (PI) f)))
(/ 2 (* (PI) f))
2
(* (PI) f)
(PI)
f
(log 1/2)
1/2
(/ (PI) -4)
-4

Outputs
(/ 4 (/ 1 (/ (log (tanh (/ f (/ 4 (PI))))) (PI))))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
4
#s(literal 4 binary64)
(/ 1 (/ (log (tanh (/ f (/ 4 (PI))))) (PI)))
(/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
1
#s(literal 1 binary64)
(/ (log (tanh (/ f (/ 4 (PI))))) (PI))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
(log (tanh (/ f (/ 4 (PI)))))
(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
(tanh (/ f (/ 4 (PI))))
(tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
(/ f (/ 4 (PI)))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
f
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
(PI)
(PI.f64)
(/ -4 (/ (PI) (log (/ (/ 4 f) (PI)))))
(.f64 (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))) (/.f64 #s(literal -4 binary64) (PI.f64)))
-4
#s(literal -4 binary64)
(/ (PI) (log (/ (/ 4 f) (PI))))
(/.f64 (PI.f64) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))))
(PI)
(PI.f64)
(log (/ (/ 4 f) (PI)))
(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
(/ (/ 4 f) (PI))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 f)
(/.f64 #s(literal 4 binary64) f)
4
#s(literal 4 binary64)
f
(/ (/ 4 (PI)) (/ 1 (log (/ f (/ 4 (PI))))))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
(/ 1 (log (/ f (/ 4 (PI)))))
(/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
1
#s(literal 1 binary64)
(log (/ f (/ 4 (PI))))
(log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
(/ f (/ 4 (PI)))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
f
(/ (log (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f)) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) f) (.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (.f64 (.f64 f f) (.f64 f (.f64 (PI.f64) #s(literal -1/12 binary64)))))) (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (.f64 f (.f64 (PI.f64) #s(literal -1/12 binary64))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f))
(log.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) f) (.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (.f64 (.f64 f f) (.f64 f (.f64 (PI.f64) #s(literal -1/12 binary64)))))) (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (.f64 f (.f64 (PI.f64) #s(literal -1/12 binary64)))))))
(/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f)
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) f) (.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (.f64 (.f64 f f) (.f64 f (.f64 (PI.f64) #s(literal -1/12 binary64)))))) (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (.f64 f (.f64 (PI.f64) #s(literal -1/12 binary64))))))
(/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f))))
(/.f64 (+.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (.f64 (.f64 f f) (.f64 f (.f64 f (.f64 (PI.f64) #s(literal -1/12 binary64))))))) (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal -1/12 binary64))))))
(- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f))))
(+.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (.f64 (.f64 f f) (.f64 f (.f64 f (.f64 (PI.f64) #s(literal -1/12 binary64)))))))
(/ (/ -4 (PI)) (/ (PI) -4))
(/.f64 #s(literal 16 binary64) (*.f64 (PI.f64) (PI.f64)))
(/ -4 (PI))
(/.f64 #s(literal -4 binary64) (PI.f64))
-4
#s(literal -4 binary64)
(PI)
(PI.f64)
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
(* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))
(.f64 (.f64 f f) (.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64))))))
(* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f))
(.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64))))
(+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI)))
(*.f64 (PI.f64) #s(literal 1/12 binary64))
(* (PI) 1/8)
(*.f64 (PI.f64) #s(literal 1/8 binary64))
1/8
#s(literal 1/8 binary64)
(/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))
(*.f64 (PI.f64) #s(literal -1/24 binary64))
(* -2 (* (* (PI) (PI)) 1/48))
(.f64 (PI.f64) (.f64 (PI.f64) #s(literal -1/24 binary64)))
-2
#s(literal -2 binary64)
(* (* (PI) (PI)) 1/48)
(.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))
(* (PI) (PI))
(*.f64 (PI.f64) (PI.f64))
1/48
#s(literal 1/48 binary64)
(* f f)
(*.f64 f f)
f
(- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))
(+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal -1/12 binary64)))))
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(/ (- (log (/ 2 (* (PI) f))) (log 1/2)) (/ (PI) -4))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(- (log (/ 2 (* (PI) f))) (log 1/2))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))) (log.f64 #s(literal 1/2 binary64)))
(log (/ 2 (* (PI) f)))
(log.f64 (/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64))))
(/ 2 (* (PI) f))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
2
#s(literal 2 binary64)
(* (PI) f)
(*.f64 f (PI.f64))
(PI)
(PI.f64)
f
(log 1/2)
(log.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)

localize338.0ms (1.7%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 (PI.f64) f)
✓	accuracy	99.5%	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))
✓	accuracy	99.4%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.4%	(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	98.5%	(+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64)))
✓	accuracy	98.5%	(.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	99.3%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.7%	(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
✓	accuracy	99.6%	(/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
✓	accuracy	99.5%	(/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))
✓	accuracy	97.7%	(PI.f64)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)))
✓	accuracy	99.4%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	97.7%	(PI.f64)

Results

153.0ms	248×	0	valid
68.0ms	6×	5	exit
9.0ms	1×	5	valid
3.0ms	1×	3	valid

Compiler

Compiled 634 to 50 computations (92.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 168.0ms

ival-log: 67.0ms (39.9% of total)

ival-div: 39.0ms (23.2% of total)

ival-tanh: 27.0ms (16.1% of total)

ival-mult: 15.0ms (8.9% of total)

backward-pass: 8.0ms (4.8% of total)

ival-sub: 4.0ms (2.4% of total)

...c/correct-round.rkt:119:19: 4.0ms (2.4% of total)

const: 1.0ms (0.6% of total)

ival-pi: 1.0ms (0.6% of total)

ival-add: 1.0ms (0.6% of total)

series111.0ms (0.6%)

Counts

24 → 240

Calls

Call 1

Inputs
#<alt (/ 4 (/ 1 (/ (log (tanh (/ f (/ 4 (PI))))) (PI))))>
#<alt (/ 1 (/ (log (tanh (/ f (/ 4 (PI))))) (PI)))>
#<alt (/ (log (tanh (/ f (/ 4 (PI))))) (PI))>
#<alt (log (tanh (/ f (/ 4 (PI)))))>
#<alt (/ -4 (/ (PI) (log (/ (/ 4 f) (PI)))))>
#<alt (/ (PI) (log (/ (/ 4 f) (PI))))>
#<alt (PI)>
#<alt (log (/ (/ 4 f) (PI)))>
#<alt (/ (/ 4 (PI)) (/ 1 (log (/ f (/ 4 (PI))))))>
#<alt (/ 4 (PI))>
#<alt (/ 1 (log (/ f (/ 4 (PI)))))>
#<alt (/ (log (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f)) (/ (PI) -4))>
#<alt (log (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f))>
#<alt (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f)>
#<alt (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f))))>
#<alt (/ (- (log (/ 2 (* (PI) f))) (log 1/2)) (/ (PI) -4))>
#<alt (- (log (/ 2 (* (PI) f))) (log 1/2))>
#<alt (log (/ 2 (* (PI) f)))>
#<alt (/ 2 (* (PI) f))>
#<alt (/ f (/ 4 (PI)))>
#<alt (/ (/ 4 f) (PI))>
#<alt (* (* (PI) (PI)) 1/48)>
#<alt (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI)))>
#<alt (* (PI) f)>

Outputs
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (/ (PI) (+ (log f) (log (* 1/4 (PI)))))>
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#<alt (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (+ (* -1 (log (/ -1 f))) (* 4 (/ 1 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))))>
#<alt (- (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (+ (* -1 (log (/ -1 f))) (/ 4 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI)))))))) (/ 8 (* (pow f 4) (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2)))))>
#<alt (- (+ (log (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI))))) (+ (* -1 (log (/ -1 f))) (+ (* 64/3 (/ 1 (* (pow f 6) (* (pow (PI) 3) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 3))))) (/ 4 (* (pow f 2) (* (PI) (+ (* -1/24 (PI)) (* 1/8 (PI))))))))) (* 8 (/ 1 (* (pow f 4) (* (pow (PI) 2) (pow (+ (* -1/24 (PI)) (* 1/8 (PI))) 2))))))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI)))) f)>
#<alt (/ (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI)))) f)>
#<alt (/ (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI)))) f)>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* f (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* f (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* f (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* f (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (/ 4 (PI))>
#<alt (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI))))>
#<alt (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI))))>
#<alt (+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2)) (PI)))>
#<alt (* -4 (/ (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2)) (PI)))>
#<alt (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))>
#<alt (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))>
#<alt (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))>
#<alt (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))>
#<alt (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))>
#<alt (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))>
#<alt (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))>
#<alt (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))>
#<alt (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))>
#<alt (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))>
#<alt (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))>
#<alt (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))>
#<alt (+ (log (/ 2 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 2 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 2 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 2 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 1 f)) (log (/ 2 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 2 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 2 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 2 (PI))))>
#<alt (+ (log (/ -2 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -2 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -2 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -2 (PI))) (log (/ -1 f)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (/ 2 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>

Calls

60 calls:

Time	Variable		Point	Expression
29.0ms	f	@	0	(/ (- (log (/ 2 (* (PI) f))) (log 1/2)) (/ (PI) -4))
22.0ms	f	@	-inf	(/ (- (log (/ 2 (* (PI) f))) (log 1/2)) (/ (PI) -4))
16.0ms	f	@	-inf	(/ (/ 4 (PI)) (/ 1 (log (/ f (/ 4 (PI))))))
7.0ms	f	@	inf	(/ (- (log (/ 2 (* (PI) f))) (log 1/2)) (/ (PI) -4))
7.0ms	f	@	0	(/ (/ 4 (PI)) (/ 1 (log (/ f (/ 4 (PI))))))

rewrite382.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

3548×	`-lowering-.f32`
3548×	`-lowering-.f64`
2370×	`pow-lowering-pow.f64`
2370×	`pow-lowering-pow.f32`
2158×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	343
1	327	224
2	3109	210
0	8120	210

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 716

Calls

Call 1

Inputs
(/ 4 (/ 1 (/ (log (tanh (/ f (/ 4 (PI))))) (PI))))
(/ 1 (/ (log (tanh (/ f (/ 4 (PI))))) (PI)))
(/ (log (tanh (/ f (/ 4 (PI))))) (PI))
(log (tanh (/ f (/ 4 (PI)))))
(/ -4 (/ (PI) (log (/ (/ 4 f) (PI)))))
(/ (PI) (log (/ (/ 4 f) (PI))))
(PI)
(log (/ (/ 4 f) (PI)))
(/ (/ 4 (PI)) (/ 1 (log (/ f (/ 4 (PI))))))
(/ 4 (PI))
(/ 1 (log (/ f (/ 4 (PI)))))
(/ (log (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f)) (/ (PI) -4))
(log (/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f))
(/ (/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) f)
(/ (- (/ (/ -4 (PI)) (/ (PI) -4)) (* (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f)))) (- (/ 4 (PI)) (* (+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI))) (* f f))))
(/ (- (log (/ 2 (* (PI) f))) (log 1/2)) (/ (PI) -4))
(- (log (/ 2 (* (PI) f))) (log 1/2))
(log (/ 2 (* (PI) f)))
(/ 2 (* (PI) f))
(/ f (/ 4 (PI)))
(/ (/ 4 f) (PI))
(* (* (PI) (PI)) 1/48)
(+ (* (PI) 1/8) (/ (* -2 (* (* (PI) (PI)) 1/48)) (PI)))
(* (PI) f)

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 4 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 4 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal -4 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 4 binary64))))
(/.f64 (*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
(/.f64 (*.f64 #s(literal 4 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (PI.f64))
(pow.f64 (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 4 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 4 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(*.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 4 binary64))
(*.f64 #s(literal -4 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(.f64 (.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))) #s(literal -1 binary64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)))
(/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 #s(literal -1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(*.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))) #s(literal -1 binary64))))
(neg.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
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(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 4 binary64) f))
(*.f64 (/.f64 #s(literal 1 binary64) f) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) f) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) f) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) f)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) f)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) f)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) f)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (/.f64 f #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(.f64 (pow.f64 (.f64 (/.f64 f #s(literal 4 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (/.f64 f #s(literal 4 binary64)) (sqrt.f64 (PI.f64))) #s(literal -1 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 f #s(literal -4 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64)))
(.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))
(.f64 #s(literal 1/48 binary64) (.f64 (PI.f64) (PI.f64)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (PI.f64))
(+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(+.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(-.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -1/24 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))))
(-.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) #s(literal 2 binary64)) (PI.f64)))
(-.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))))) (/.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (PI.f64) #s(literal 1/8 binary64) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))))
(fma.f64 #s(literal 1/8 binary64) (PI.f64) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))))
(fma.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)) (.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (/.f64 #s(literal -2 binary64) (PI.f64)) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (PI.f64))) (.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/24 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(fma.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/24 binary64)) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1/48 binary64) (PI.f64)) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1 binary64) (PI.f64))) (.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 #s(literal -2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (cbrt.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 #s(literal -2 binary64) (sqrt.f64 (PI.f64))) (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (sqrt.f64 (PI.f64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) (PI.f64)) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal -2 binary64) (cbrt.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64)) (/.f64 #s(literal 1/48 binary64) (PI.f64)) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 1/48 binary64) (cbrt.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1/48 binary64) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))
(fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) (.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (-.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (.f64 (PI.f64) #s(literal 1/8 binary64))))) (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/512 binary64)) (.f64 #s(literal -8 binary64) (.f64 #s(literal 1/110592 binary64) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (*.f64 (PI.f64) #s(literal 1/48 binary64)))))))
(/.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/512 binary64)) (.f64 #s(literal -8 binary64) (.f64 #s(literal 1/110592 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))) (+.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (-.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (*.f64 (PI.f64) #s(literal 1/8 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/512 binary64)) (.f64 #s(literal -8 binary64) (.f64 #s(literal 1/110592 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))) (+.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/24 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (.f64 (PI.f64) #s(literal 1/48 binary64))))) (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64)))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/512 binary64)) (.f64 #s(literal -8 binary64) (.f64 #s(literal 1/110592 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))))) (neg.f64 (+.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (-.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (*.f64 (PI.f64) #s(literal 1/8 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (.f64 (PI.f64) #s(literal 1/48 binary64)))))) (neg.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64))) (-.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (*.f64 (PI.f64) #s(literal 1/8 binary64))))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (-.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (.f64 (PI.f64) #s(literal 1/8 binary64))))) (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/512 binary64)) (.f64 #s(literal -8 binary64) (.f64 #s(literal 1/110592 binary64) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (*.f64 (PI.f64) #s(literal 1/48 binary64)))))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/512 binary64)) (.f64 #s(literal -8 binary64) (.f64 #s(literal 1/110592 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (-.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))) (.f64 (PI.f64) #s(literal 1/8 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/64 binary64)) (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/48 binary64)) (.f64 (PI.f64) #s(literal 1/48 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 f (PI.f64)))
(*.f64 f (PI.f64))
(*.f64 (PI.f64) f)
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) f))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) f))
(.f64 (.f64 f #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 f (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))

simplify316.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

3732×	`-lowering-.f32`
3732×	`-lowering-.f64`
1818×	`+-lowering-+.f64`
1818×	`+-lowering-+.f32`
1798×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	382	4692
1	1293	4139
2	5549	4133
0	8043	4133

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(/ (PI) (+ (log f) (log (* 1/4 (PI)))))
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(* f (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(* f (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(* f (+ (* -1/24 (PI)) (* 1/8 (PI))))
(* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(* -1 (* f (- (* -1 (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(/ 4 (PI))
(+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI))))
(+ (* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI)))) (* 4 (/ 1 (PI))))
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(* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))
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(- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))
(- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))
(- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))
(- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))
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(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(+ (log (/ 2 (PI))) (* -1 (log f)))
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(+ (log (/ 1 f)) (log (/ 2 (PI))))
(+ (log (/ 1 f)) (log (/ 2 (PI))))
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(+ (log (/ 1 f)) (log (/ 2 (PI))))
(+ (log (/ -2 (PI))) (log (/ -1 f)))
(+ (log (/ -2 (PI))) (log (/ -1 f)))
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(+ (log (/ -2 (PI))) (log (/ -1 f)))
(/ 2 (* f (PI)))
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(/ 2 (* f (PI)))
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(/ 2 (* f (PI)))
(/ 2 (* f (PI)))
(/ 2 (* f (PI)))
(* 1/4 (* f (PI)))
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(* 1/4 (* f (PI)))
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(* 1/4 (* f (PI)))
(* 1/4 (* f (PI)))
(/ 4 (* f (PI)))
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(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))

Outputs
(* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))
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(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
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(* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))
(.f64 (.f64 (PI.f64) (*.f64 f f)) #s(literal 1/12 binary64))
(* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (*.f64 f f)))))
(* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (*.f64 f f)))))
(* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (*.f64 f f)))))
(* (pow f 2) (+ (* -1/24 (PI)) (* 1/8 (PI))))
(.f64 (.f64 (PI.f64) (*.f64 f f)) #s(literal 1/12 binary64))
(* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (*.f64 f f)))))
(* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (*.f64 f f)))))
(* (pow f 2) (+ (* -1/24 (PI)) (+ (* 1/8 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (*.f64 f f)))))
(* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))) (PI.f64))
(* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))) (PI.f64))
(* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))) (PI.f64))
(* -4 (/ (- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))) (PI.f64))
(* -4 (/ (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))) (PI.f64))
(* -4 (/ (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))) (PI.f64))
(* -4 (/ (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))) (PI.f64))
(* -4 (/ (- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))) (PI.f64))
(* -4 (/ (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (+.f64 (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal 1/2 binary64))))) (PI.f64))
(* -4 (/ (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (+.f64 (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal 1/2 binary64))))) (PI.f64))
(* -4 (/ (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (+.f64 (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal 1/2 binary64))))) (PI.f64))
(* -4 (/ (- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2)) (PI)))
(/.f64 (*.f64 #s(literal -4 binary64) (+.f64 (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal 1/2 binary64))))) (PI.f64))
(- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))
(-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))
(-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))
(-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log (/ 2 (PI))) (* -1 (log f))) (log 1/2))
(-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))
(-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))
(-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))
(-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))
(-.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(+.f64 (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal 1/2 binary64))))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(+.f64 (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal 1/2 binary64))))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(+.f64 (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal 1/2 binary64))))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(+.f64 (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal 1/2 binary64))))
(+ (log (/ 2 (PI))) (* -1 (log f)))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 2 (PI))) (* -1 (log f)))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 2 (PI))) (* -1 (log f)))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 2 (PI))) (* -1 (log f)))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 1 f)) (log (/ 2 (PI))))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 1 f)) (log (/ 2 (PI))))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 1 f)) (log (/ 2 (PI))))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 1 f)) (log (/ 2 (PI))))
(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ -2 (PI))) (log (/ -1 f)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))))
(+ (log (/ -2 (PI))) (log (/ -1 f)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))))
(+ (log (/ -2 (PI))) (log (/ -1 f)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))))
(+ (log (/ -2 (PI))) (log (/ -1 f)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -2 binary64) (PI.f64))))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(/ 2 (* f (PI)))
(/.f64 #s(literal 2 binary64) (*.f64 f (PI.f64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))
(* f (PI))
(*.f64 f (PI.f64))

eval452.0ms (2.3%)

Compiler: Compiled 96473 to 9662 computations (90% saved)

prune356.0ms (1.8%)

Pruning

21 alts after pruning (14 fresh and 7 done)

	Pruned	Kept	Total
New	2171	5	2176
Fresh	4	9	13
Picked	1	4	5
Done	0	3	3
Total	2176	21	2197

Accuracy

100.0%

Counts

2197 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.9%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) #s(literal -1/4 binary64)) (PI.f64))
	94.8%	(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
✓	94.7%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	94.8%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.4%	(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 (.f64 f f) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 f f))))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.4%	(/.f64 (log.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (*.f64 f f)) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.4%	(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
	1.6%	(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	99.0%	(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal 4 binary64)))
	10.1%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f)))))) (log1p.f64 (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))))))
	94.9%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))))
✓	99.3%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
✓	99.3%	(/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))))
	94.8%	(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
	94.8%	(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64))))))
✓	94.8%	(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
✓	94.7%	(-.f64 (/.f64 (/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64)) #s(literal -1/4 binary64)))
	94.8%	(+.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64)))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 f)))
	94.4%	(.f64 (/.f64 #s(literal -4 binary64) (cbrt.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
	94.9%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
✓	94.8%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))

Compiler

Compiled 1435 to 539 computations (62.4% saved)

regimes102.0ms (0.5%)

Counts

54 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 0 binary64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (*.f64 f f)) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 (.f64 f f) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 f f))))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))))
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))))
(/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(.f64 (/.f64 #s(literal -4 binary64) (cbrt.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
(+.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64)))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 f)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f))))
(-.f64 (/.f64 (/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64)) #s(literal -1/4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64)))
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64))))
(/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f)))))) (log1p.f64 (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))))))
(/.f64 (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))) (log1p.f64 (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))
(-.f64 (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)) #s(literal -1/4 binary64)))
(/.f64 (-.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))) (*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (.f64 #s(literal 0 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Outputs
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))

Calls

6 calls:

30.0ms	f
19.0ms	(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)
14.0ms	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))
12.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))
11.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))

Results

Accuracy	Segments	Branch
99.4%	1	`f`
99.4%	1	`(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))`
99.4%	1	`(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))`
99.4%	1	`(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))`
99.4%	1	`(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))`
99.4%	1	`(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)`

Compiler

Compiled 144 to 60 computations (58.3% saved)

regimes9.0ms (0%)

Counts

24 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 0 binary64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (*.f64 f f)) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 (.f64 f f) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 f f))))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))))

Outputs
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
99.3%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes22.0ms (0.1%)

Counts

22 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 0 binary64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (*.f64 f f)) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 (.f64 f f) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 f f))))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f)))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64))))))

Outputs

(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (+.f64 (*.f64 (PI.f64) #s(literal 1/8 binary64)) (*.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 (*.f64 f f) (*.f64 (+.f64 (*.f64 (PI.f64) #s(literal 1/8 binary64)) (*.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 (+.f64 (*.f64 (PI.f64) #s(literal 1/8 binary64)) (*.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
95.4%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0%)

Counts

17 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 0 binary64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (*.f64 f f)) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) (.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))

Outputs

(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 (+.f64 (*.f64 (PI.f64) #s(literal 1/8 binary64)) (*.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
95.4%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

14 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 0 binary64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (*.f64 f f)) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))

Outputs
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
95.4%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

12 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 0 binary64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))

Outputs
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
94.9%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs

(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))

(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))

(/.f64 (log.f64 (*.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Outputs
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
94.8%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))

Outputs
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
94.8%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

48×	`*-commutative_binary64`
36×	`+-commutative_binary64`
30×	`sub-neg_binary64`
26×	`neg-sub0_binary64`
26×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	152
1	79	152
2	103	152
3	138	152
4	164	152
5	180	152
6	187	152
7	188	152

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 (.f64 f f) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 f f))))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))

Outputs
(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 (log.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 (.f64 f f) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (.f64 f f))))) (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 f (+.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -2 binary64) (.f64 (PI.f64) #s(literal 1/48 binary64)))) (*.f64 f f)) (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (.f64 f (*.f64 (PI.f64) #s(literal 1/12 binary64))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64)))))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))))
(*.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))) (/.f64 #s(literal -4 binary64) (PI.f64)))

soundness3.7s (19.3%)

Rules

4244×	`-lowering-.f32`
4244×	`-lowering-.f64`
4240×	`/-lowering-/.f32`
4240×	`/-lowering-/.f64`
4210×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	343
1	327	224
2	3109	210
0	8120	210
0	227	3413
1	749	3003
2	3265	2881
0	8978	2881
0	37	176
1	210	157
2	1493	155
0	8271	155
0	29	202
1	191	98
2	1475	98
0	8243	98
0	367	4118
1	1248	3674
2	5396	3658
0	8308	3658
0	54	283
1	314	245
2	3012	244
0	8960	244
0	16	36
1	46	32
2	123	32
3	271	32
4	464	32
5	679	32
6	913	32
7	1218	32
8	1868	32
9	2313	32
10	3051	32
11	4744	32
12	5300	32
13	5563	32
14	6101	32
15	7504	32
0	8030	32

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 219 to 110 computations (49.8% saved)

preprocess52.0ms (0.3%)

Compiler: Compiled 382 to 144 computations (62.3% saved)

analyze369.0ms (1.9%)

sample5.6s (29%)

preprocess293.0ms (1.5%)

explain344.0ms (1.8%)

eval6.0ms (0%)

prune1.0ms (0%)

simplify146.0ms (0.8%)

localize282.0ms (1.5%)

series208.0ms (1.1%)

rewrite433.0ms (2.2%)

simplify232.0ms (1.2%)

eval249.0ms (1.3%)

prune175.0ms (0.9%)

simplify207.0ms (1.1%)

localize381.0ms (2%)

series309.0ms (1.6%)

rewrite466.0ms (2.4%)

simplify311.0ms (1.6%)

eval424.0ms (2.2%)

prune310.0ms (1.6%)

simplify195.0ms (1%)

localize316.0ms (1.6%)

series264.0ms (1.4%)

rewrite427.0ms (2.2%)

simplify307.0ms (1.6%)

eval536.0ms (2.8%)

prune255.0ms (1.3%)

simplify437.0ms (2.3%)

localize338.0ms (1.7%)

series111.0ms (0.6%)

rewrite382.0ms (2%)

simplify316.0ms (1.6%)

eval452.0ms (2.3%)

prune356.0ms (1.8%)

regimes102.0ms (0.5%)

regimes9.0ms (0%)

regimes22.0ms (0.1%)

regimes7.0ms (0%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify13.0ms (0.1%)

soundness3.7s (19.3%)

preprocess52.0ms (0.3%)

end0.0ms (0%)

Profiling