Metrics for VandenBroeck and Keller, Equation (20)

analyze287.0ms (1.3%)

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: 142.0ms

ival-div: 36.0ms (25.4% of total)

ival-exp: 23.0ms (16.2% of total)

ival-mult: 23.0ms (16.2% of total)

ival-neg: 16.0ms (11.3% of total)

ival-log: 13.0ms (9.2% of total)

ival-add: 10.0ms (7.1% of total)

ival-sub: 9.0ms (6.3% of total)

ival-pi: 8.0ms (5.6% of total)

const: 3.0ms (2.1% of total)

backward-pass: 1.0ms (0.7% of total)

sample6.4s (30.1%)

Results

2.7s	7248×	1	invalid
2.6s	7691×	1	valid
208.0ms	184×	2	valid
74.0ms	381×	0	valid
1.0ms	5×	0	invalid
0.0ms	3×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 4.3s

ival-exp: 970.0ms (22.8% of total)

ival-div: 722.0ms (17% of total)

ival-mult: 583.0ms (13.7% of total)

backward-pass: 511.0ms (12% of total)

ival-log: 418.0ms (9.8% of total)

ival-neg: 369.0ms (8.7% of total)

ival-pi: 263.0ms (6.2% of total)

ival-add: 216.0ms (5.1% of total)

ival-sub: 158.0ms (3.7% of total)

const: 49.0ms (1.2% of total)

Bogosity

preprocess301.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

2134×	`sum3-define`
2054×	`fnmadd-define`
1954×	`fnmadd-define`
1940×	`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	78
11	7328	60
12	7999	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	5297	32
13	5531	32
14	5938	32
15	7040	32
0	8021	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 (*.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (*.f64 (PI.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))))))

explain389.0ms (1.8%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
243	-	1	(0.009253125907942245)	`(-.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	-	0	-	`(/.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)))))`
2	-	0	-	`(exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))`
2	-	0	-	`(exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))`
1	-	0	-	`(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	-	0	-	`(PI.f64)`
0	-	0	-	`(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)`
0	-	0	-	`(neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))`
0	-	0	-	`(/.f64 (PI.f64) #s(literal 4 binary64))`
0	-	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	-	0	-	`f`
0	-	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	-	0	-	`#s(literal 4 binary64)`
0	-	0	-	`(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))`
0	-	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	-	0	-	`#s(literal 1 binary64)`

Results

264.0ms	468×	1	valid
23.0ms	18×	2	valid
6.0ms	26×	0	valid

Compiler

Compiled 434 to 50 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-exp: 33.0ms (22% of total)

backward-pass: 26.0ms (17.3% of total)

ival-div: 23.0ms (15.3% of total)

ival-mult: 22.0ms (14.6% of total)

ival-log: 18.0ms (12% of total)

ival-neg: 9.0ms (6% of total)

ival-sub: 6.0ms (4% of total)

ival-add: 6.0ms (4% of total)

ival-pi: 5.0ms (3.3% of total)

const: 2.0ms (1.3% of total)

eval0.0ms (0%)

Compiler: Compiled 33 to 15 computations (54.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.7%	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	7.7%	(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

▶

7.7%

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

▶

7.7%

(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 31 computations (56.3% saved)

simplify161.0ms (0.8%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (exp.f64 (/.f64 (.f64 (PI.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 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.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 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.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 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.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	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)))))))
✓	cost-diff	64	(neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))
✓	cost-diff	64	(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))))))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))

Rules

2134×	`sum3-define`
2054×	`fnmadd-define`
1936×	`fma-define`
1440×	`sum5-define`
1176×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	350
1	70	322
2	161	322
3	314	322
4	502	322
5	717	322
6	953	322
7	1240	322
8	1892	322
9	2332	322
10	3068	322
11	4761	322
12	5318	322
13	5547	322
14	5954	322
15	7056	322
0	8008	322

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

localize707.0ms (3.3%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 (PI.f64) f)
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.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	96.6%	(/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
✓	accuracy	12.7%	(-.f64 (exp.f64 (/.f64 (.f64 (PI.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	96.6%	(/.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	12.7%	(-.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

281.0ms	236×	1	valid
23.0ms	9×	2	valid
4.0ms	11×	0	valid

Compiler

Compiled 343 to 29 computations (91.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 132.0ms

ival-div: 31.0ms (23.5% of total)

ival-exp: 31.0ms (23.5% of total)

backward-pass: 18.0ms (13.7% of total)

ival-mult: 17.0ms (12.9% of total)

ival-log: 17.0ms (12.9% of total)

ival-add: 6.0ms (4.6% of total)

ival-sub: 5.0ms (3.8% of total)

ival-neg: 5.0ms (3.8% of total)

ival-pi: 3.0ms (2.3% of total)

const: 1.0ms (0.8% of total)

series502.0ms (2.3%)

Counts

13 → 144

Calls

Call 1

Inputs
#<alt (/ 1 (/ (PI) 4))>
#<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 (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 (/ (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 (* -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 (/ 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 (* -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
341.0ms	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))))))))
63.0ms	f	@	-inf	(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
35.0ms	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))))))))
27.0ms	f	@	inf	(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
23.0ms	f	@	0	(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))

rewrite375.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3276×	`-lowering-.f32`
3276×	`-lowering-.f64`
1814×	`/-lowering-/.f32`
1814×	`/-lowering-/.f64`
1156×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	200
1	150	95
2	786	92
3	4076	92
0	8383	92

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 997

Calls

Call 1

Inputs
(/ 1 (/ (PI) 4))
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))
(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
(exp.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -4 binary64) (PI.f64)))
(neg.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))))
(/.f64 #s(literal 4 binary64) (PI.f64))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1 binary64))
(/.f64 #s(literal -4 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 #s(literal -1 binary64) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(/.f64 (pow.f64 (PI.f64) #s(literal -2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)))
(/.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64)))
(/.f64 (/.f64 #s(literal -4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal -1/4 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (neg.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (neg.f64 (/.f64 #s(literal -4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (neg.f64 (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
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(+.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))) #s(literal -1 binary64)))
(-.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))
(-.f64 #s(literal 0 binary64) (log.f64 (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(-.f64 (log.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (log.f64 #s(literal -1 binary64)))
(neg.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))
(neg.f64 (log.f64 (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)))
(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
(/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 1 binary64))
(/.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))) #s(literal -1 binary64))
(/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (*.f64 (PI.f64) f)))
(/.f64 (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) f)) #s(literal -4 binary64))
(/.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) f))
(/.f64 (-.f64 #s(literal 0 binary64) f) (/.f64 #s(literal -4 binary64) (PI.f64)))
(/.f64 (/.f64 f #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) f)) (/.f64 #s(literal 4 binary64) (PI.f64)))
(/.f64 (/.f64 f #s(literal 1 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64)))
(/.f64 (/.f64 f #s(literal -1 binary64)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(/.f64 (/.f64 f (/.f64 #s(literal 1 binary64) (PI.f64))) #s(literal 4 binary64))
(/.f64 (/.f64 f (/.f64 #s(literal -1 binary64) (PI.f64))) #s(literal -4 binary64))
(pow.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
(*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))
(*.f64 (PI.f64) (log.f64 (exp.f64 (/.f64 f #s(literal 4 binary64)))))
(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)
(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (exp.f64 f)))
(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) f)))
(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (/.f64 f #s(literal 1 binary64)))
(*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))
(*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)) #s(literal 1 binary64))
(*.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))) #s(literal -1 binary64))
(.f64 (.f64 (PI.f64) f) #s(literal 1/4 binary64))
(.f64 (.f64 (PI.f64) f) (log.f64 (exp.f64 #s(literal 1/4 binary64))))
(*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (-.f64 #s(literal 0 binary64) f))
(*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (exp.f64 (-.f64 #s(literal 0 binary64) f))))
(*.f64 #s(literal -1 binary64) (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 f #s(literal 4 binary64))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) (/.f64 (*.f64 f (cbrt.f64 (PI.f64))) #s(literal 4 binary64))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (*.f64 f (sqrt.f64 (PI.f64))) #s(literal 4 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (.f64 f (cbrt.f64 (PI.f64))) #s(literal 4 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (/.f64 (.f64 f (cbrt.f64 (PI.f64))) #s(literal -4 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)) f))
(.f64 (sqrt.f64 (PI.f64)) (/.f64 (.f64 f (sqrt.f64 (PI.f64))) #s(literal 4 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (neg.f64 (/.f64 (.f64 f (sqrt.f64 (PI.f64))) #s(literal -4 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64)) f))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 f #s(literal -4 binary64)))
(.f64 (.f64 (PI.f64) (-.f64 #s(literal 0 binary64) f)) #s(literal -1/4 binary64))
(.f64 #s(literal -1/4 binary64) (.f64 (PI.f64) (-.f64 #s(literal 0 binary64) f)))
(.f64 #s(literal -1/4 binary64) (log.f64 (exp.f64 (.f64 (PI.f64) (-.f64 #s(literal 0 binary64) f)))))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (PI.f64) f) #s(literal 1 binary64)))
(*.f64 #s(literal 1/4 binary64) (/.f64 f (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (-.f64 #s(literal 0 binary64) f) (/.f64 (PI.f64) #s(literal -4 binary64)))
(*.f64 (/.f64 f #s(literal -4 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (/.f64 f #s(literal 4 binary64)) (PI.f64))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (*.f64 f (sqrt.f64 (PI.f64))) #s(literal 4 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (.f64 f (cbrt.f64 (PI.f64))) #s(literal -4 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (/.f64 (.f64 f (sqrt.f64 (PI.f64))) #s(literal -4 binary64)))
(.f64 (.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)))
(.f64 (.f64 f (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64)))
(.f64 (/.f64 (.f64 f (cbrt.f64 (PI.f64))) #s(literal 4 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (/.f64 (.f64 f (cbrt.f64 (PI.f64))) #s(literal 4 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(.f64 (/.f64 (.f64 f (sqrt.f64 (PI.f64))) #s(literal 4 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)) (log.f64 (exp.f64 (.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64)) (.f64 f (sqrt.f64 (PI.f64))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64)) (log.f64 (exp.f64 (.f64 f (sqrt.f64 (PI.f64))))))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) f)) (/.f64 (PI.f64) #s(literal 4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (PI.f64))) (/.f64 f #s(literal -4 binary64)))
(*.f64 (/.f64 f #s(literal 1 binary64)) (/.f64 (PI.f64) #s(literal 4 binary64)))
(*.f64 (/.f64 f #s(literal -1 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(*.f64 (/.f64 f (/.f64 #s(literal 1 binary64) (PI.f64))) #s(literal 1/4 binary64))
(*.f64 (/.f64 f (/.f64 #s(literal -1 binary64) (PI.f64))) #s(literal -1/4 binary64))
(.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 f (cbrt.f64 (PI.f64))))
(.f64 (.f64 #s(literal 1/4 binary64) (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 1/4 binary64) (*.f64 f (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (/.f64 f #s(literal 4 binary64)) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (/.f64 f #s(literal 4 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(+.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(+.f64 (*.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) (fma.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 1 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(+.f64 (*.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) (fma.f64 #s(literal -1 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(+.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(+.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(+.f64 (fma.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 1 binary64) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal -1 binary64)))) (fma.f64 (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))) #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal -1 binary64))))
(-.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))
(-.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (/.f64 (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(-.f64 (+.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 0 binary64)) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(fma.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(fma.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 1 binary64) (neg.f64 (/.f64 (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))) #s(literal 1 binary64))))
(fma.f64 (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))) #s(literal -1 binary64) (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(fma.f64 #s(literal -1 binary64) (exp.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))) (exp.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(neg.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(/.f64 (*.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal -1 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal -1/2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
(*.f64 #s(literal 2 binary64) (/.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 1 binary64)))
(*.f64 (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 2 binary64))
(.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(*.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))
(log.f64 (exp.f64 (*.f64 (PI.f64) f)))
(-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) f)))
(neg.f64 (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) f)))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) f))
(*.f64 (PI.f64) f)
(*.f64 (PI.f64) (log.f64 (exp.f64 f)))
(*.f64 (PI.f64) (neg.f64 (-.f64 #s(literal 0 binary64) f)))
(*.f64 f (PI.f64))
(.f64 (.f64 (PI.f64) f) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (PI.f64) (-.f64 #s(literal 0 binary64) f)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 f (cbrt.f64 (PI.f64)))))
(.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 f (sqrt.f64 (PI.f64)))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 f (cbrt.f64 (PI.f64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) f)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 f (sqrt.f64 (PI.f64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) f)))
(.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (.f64 f (sqrt.f64 (PI.f64))))))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) f))
(.f64 (.f64 (PI.f64) (-.f64 #s(literal 0 binary64) f)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) f) (-.f64 #s(literal 0 binary64) (PI.f64)))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 f (sqrt.f64 (PI.f64)))))
(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (.f64 (cbrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) f)))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) f)))
(.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)))
(.f64 (.f64 f (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 f (cbrt.f64 (PI.f64))) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) f)) (PI.f64))
(.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) f)) (PI.f64))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1 binary64)) f)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(.f64 (.f64 (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 f (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 f (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 f (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))

simplify244.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

3144×	`-lowering-.f32`
3144×	`-lowering-.f64`
1566×	`+-lowering-+.f64`
1566×	`+-lowering-+.f32`
1430×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	3085
1	749	2697
2	3270	2597
0	8945	2597

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))))
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(/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (neg (* 1/4 (* f (PI))))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (neg (* 1/4 (* f (PI)))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* 1/4 (* f (PI)))
(.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))
(* f (- (* 1/4 (PI)) (* -1/4 (PI))))
(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f)
(* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))
(.f64 f (+.f64 (.f64 f (.f64 f (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/192 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(* 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))))
(.f64 f (+.f64 (.f64 (.f64 f f) (+.f64 (.f64 f (.f64 f (.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/61440 binary64)))) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/192 binary64))))) (.f64 (PI.f64) #s(literal 1/2 binary64))))
(* 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))))
(.f64 f (+.f64 (.f64 (.f64 f f) (+.f64 (.f64 (.f64 f f) (+.f64 (.f64 f (.f64 f (.f64 (pow.f64 (PI.f64) #s(literal 7 binary64)) #s(literal 1/41287680 binary64)))) (.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/61440 binary64)))) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/192 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)

eval334.0ms (1.6%)

Compiler: Compiled 56702 to 6354 computations (88.8% saved)

prune196.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	1725	17	1742
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	1727	17	1744

Accuracy

99.6%

Counts

1744 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.4%	(fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 #s(literal -4 binary64) (PI.f64)) (neg.f64 (/.f64 (log.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
	98.2%	(/.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
▶	99.1%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
	99.0%	(/.f64 (/.f64 #s(literal 1 binary64) (/.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)))
	98.9%	(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
	95.8%	(/.f64 (-.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.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 f (/.f64 #s(literal -4 binary64) (PI.f64)))))))) (*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))))
▶	94.4%	(/.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)))
	99.0%	(/.f64 (-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	99.1%	(/.f64 (+.f64 (log.f64 (/.f64 (/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	98.8%	(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (sqrt.f64 (PI.f64)))
	95.0%	(/.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)))
	96.0%	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (*.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	94.3%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	98.9%	(/.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))))))
▶	95.7%	(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
	98.8%	(*.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))))
	94.2%	(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) f)))))

Compiler

Compiled 678 to 490 computations (27.7% saved)

simplify191.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))
✓	cost-diff	0	(log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
✓	cost-diff	0	(/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	256	(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
✓	cost-diff	0	(log.f64 (/.f64 (/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64)))
✓	cost-diff	0	(+.f64 (log.f64 (/.f64 (/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 (log.f64 (/.f64 (/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	128	(/.f64 (/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
✓	cost-diff	0	(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f))
✓	cost-diff	0	(/.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)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f)
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f)))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/2 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)))) (PI.f64))
✓	cost-diff	0	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))

Rules

2414×	`-lowering-.f32`
2414×	`-lowering-.f64`
1582×	`fnmadd-define`
1520×	`/-lowering-/.f32`
1520×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	334
1	114	310
2	291	310
3	676	308
4	1607	308
5	4531	308
0	8373	308

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize307.0ms (1.4%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(/.f64 (log.f64 (*.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	99.1%	(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
✓	accuracy	97.0%	(log.f64 (*.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
✓	accuracy	96.9%	(log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
✓	accuracy	99.6%	(/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))
✓	accuracy	99.5%	(/.f64 (+.f64 (log.f64 (/.f64 (/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))
✓	accuracy	99.4%	(+.f64 (log.f64 (/.f64 (/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.6%	(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f))
✓	accuracy	99.5%	(/.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)))
✓	accuracy	96.9%	(log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.6%	(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f)
✓	accuracy	99.6%	(/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f))
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	100.0%	(tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
✓	accuracy	99.6%	(log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))
✓	accuracy	99.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64))
✓	accuracy	99.5%	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))

Results

184.0ms	246×	0	valid
40.0ms	9×	2	valid
2.0ms	1×	1	valid

Compiler

Compiled 336 to 45 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-log: 46.0ms (43.2% of total)

ival-div: 32.0ms (30.1% of total)

ival-mult: 7.0ms (6.6% of total)

ival-tanh: 5.0ms (4.7% of total)

ival-sub: 4.0ms (3.8% of total)

ival-cosh: 4.0ms (3.8% of total)

backward-pass: 3.0ms (2.8% of total)

ival-sinh: 2.0ms (1.9% of total)

const: 1.0ms (0.9% of total)

ival-pi: 1.0ms (0.9% of total)

ival-add: 1.0ms (0.9% of total)

series468.0ms (2.2%)

Counts

26 → 276

Calls

Call 1

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

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)))) (PI))>
#<alt (+ (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))) (+ (/ (log f) (PI)) (/ (log (* 1/4 (PI))) (PI))))>
#<alt (+ (* 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))))) (PI))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))) (+ (/ (log f) (PI)) (/ (log (* 1/4 (PI))) (PI))))>
#<alt (+ (* f (+ (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* 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)))))) (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)))) (PI))))))) (+ (/ (log f) (PI)) (/ (log (* 1/4 (PI))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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))))))))>
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#<alt (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI))))))))>
#<alt (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI))))))))>
#<alt (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI))))))))>
#<alt (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI))))))))>
#<alt (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI))))))))>
#<alt (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI))))))))>
#<alt (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI))))))))>
#<alt (* -4 (/ (+ (log f) (log (* 1/2 (PI)))) (PI)))>
#<alt (+ (* -4 (/ (+ (log f) (log (* 1/2 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))>
#<alt (+ (* -4 (/ (+ (log f) (log (* 1/2 (PI)))) (PI))) (* f (+ (* -2 (/ (* f (+ (* -4 (/ (+ (* -1/192 (pow (PI) 3)) (+ (* 1/128 (pow (PI) 3)) (* 1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))))) (PI))) (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))>
#<alt (+ (* -4 (/ (+ (log f) (log (* 1/2 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* -2 (/ (+ (* -4 (/ (+ (* -1/192 (pow (PI) 3)) (+ (* 1/128 (pow (PI) 3)) (* 1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))))) (PI))) (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2)))) (PI))) (* -2/3 (/ (* f (+ (* -24 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (+ (* -1/192 (pow (PI) 3)) (+ (* 1/128 (pow (PI) 3)) (* 1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2)))))))) (pow (PI) 2))) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* -12 (/ (+ (* -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)) (* 1/4 (* (PI) (+ (* -1/384 (pow (PI) 3)) (+ (* 1/128 (pow (PI) 3)) (* 1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2)))))))))))) (PI)))))) (PI))))))))>
#<alt (* -4 (/ (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI)))))))) (PI)))>
#<alt (* -4 (/ (log (* -1 (- (exp (* -1/4 (* f (PI)))) (/ 1 (exp (* -1/4 (* f (PI)))))))) (PI)))>

Calls

69 calls:

Time	Variable		Point	Expression
87.0ms	f	@	0	(/ (- (log (/ 2 (* (PI) 1/2))) (log f)) (/ (PI) -4))
45.0ms	f	@	inf	(- (/ (log (* 2 (cosh (/ f (/ -4 (PI)))))) (/ (PI) -4)) (/ (log (* -2 (sinh (/ f (/ -4 (PI)))))) (/ (PI) -4)))
44.0ms	f	@	-inf	(- (/ (log (* 2 (cosh (/ f (/ -4 (PI)))))) (/ (PI) -4)) (/ (log (* -2 (sinh (/ f (/ -4 (PI)))))) (/ (PI) -4)))
41.0ms	f	@	inf	(/ (+ (log (/ (/ -1 (tanh (/ f (/ -4 (PI))))) 2)) (log 2)) (/ (PI) -4))
38.0ms	f	@	inf	(/ (/ (log (tanh (/ (PI) (/ 4 f)))) (PI)) 1/4)

rewrite430.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

5434×	`/-lowering-/.f32`
5434×	`/-lowering-/.f64`
3746×	`-lowering-.f32`
3746×	`-lowering-.f64`
1172×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	241
1	246	215
2	1647	213
0	8230	213

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 1414

Calls

Call 1

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

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

simplify324.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

5178×	`-lowering-.f32`
5178×	`-lowering-.f64`
2942×	`+-lowering-+.f64`
2942×	`+-lowering-+.f32`
1324×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	501	8248
1	1788	6710
0	8541	6710

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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

eval406.0ms (1.9%)

Compiler: Compiled 61193 to 7768 computations (87.3% saved)

prune274.0ms (1.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	2325	16	2341
Fresh	10	2	12
Picked	4	1	5
Done	0	0	0
Total	2339	19	2358

Accuracy

99.7%

Counts

2358 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	10.9%	(/.f64 (/.f64 (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (.f64 f (PI.f64))))))) (log1p.f64 (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (.f64 f (PI.f64))))))) (PI.f64)) #s(literal 1/4 binary64))
	94.4%	(/.f64 (/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))) (PI.f64)) #s(literal 1/4 binary64))
	94.3%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64)) #s(literal -1/4 binary64))
✓	99.1%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
	98.9%	(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
	94.3%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	94.3%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	94.3%	(/.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.0%	(/.f64 (+.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 f (+.f64 (/.f64 #s(literal 0 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 f (.f64 #s(literal 8 binary64) (+.f64 (/.f64 (+.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/128 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/384 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64))))))) (.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 0 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))))))) f)) (log.f64 #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	95.0%	(/.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)))
	93.9%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
▶	98.9%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
	94.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
	94.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64))))
▶	94.1%	(-.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)))
	94.2%	(-.f64 (/.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 16 binary64))) (/.f64 (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 f)) (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 16 binary64))))
	94.2%	(-.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (/.f64 (log.f64 f) (PI.f64)) #s(literal -1/4 binary64)))
	94.2%	(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -1 binary64)))
▶	94.2%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Compiler

Compiled 704 to 512 computations (27.3% saved)

simplify208.0ms (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	256	(-.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	(log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))
✓	cost-diff	0	(log.f64 #s(literal 2 binary64))
✓	cost-diff	0	(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))))
✓	cost-diff	0	(/.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	128	(.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
✓	cost-diff	256	(+.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	384	(.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 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 #s(literal 4 binary64) (.f64 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

3914×	`-lowering-.f32`
3914×	`-lowering-.f64`
2002×	`/-lowering-/.f32`
2002×	`/-lowering-/.f64`
1752×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	48	408
1	123	345
2	332	329
3	957	322
4	2771	281
5	6022	281
0	8397	281

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 (PI))
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
(/ (- (log 2) (log (* (PI) (* f 1/2)))) (/ (PI) -4))
(- (log 2) (log (* (PI) (* f 1/2))))
(log 2)
2
(log (* (PI) (* f 1/2)))
(* (PI) (* f 1/2))
(PI)
(* f 1/2)
f
1/2
(/ (PI) -4)
-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 (*.f64 (PI.f64) f) #s(literal 4 binary64)))) (/.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 (*.f64 (PI.f64) f) #s(literal 4 binary64)))))
(PI)
(PI.f64)
(log (tanh (/ (PI) (/ 4 f))))
(log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))
(tanh (/ (PI) (/ 4 f)))
(tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))
(/ (PI) (/ 4 f))
(/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))
(/ 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
#s(literal 4 binary64)
(* f (PI))
(*.f64 (PI.f64) f)
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 f (*.f64 f #s(literal 1/12 binary64))))) 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 f (*.f64 f #s(literal 1/12 binary64))))) 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 f (*.f64 f #s(literal 1/12 binary64))))) 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 f (*.f64 f #s(literal 1/12 binary64)))))
(/ 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 f (*.f64 f #s(literal 1/12 binary64))))
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)
(/ (- (log 2) (log (* (PI) (* f 1/2)))) (/ (PI) -4))
(/.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(- (log 2) (log (* (PI) (* f 1/2))))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))))
(log 2)
(log.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(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)))
(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)
(- (/ (/ (log 2) (PI)) -1/4) (/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4))
(/.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (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 (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) (PI.f64))
(/ (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)

localize380.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
✓	accuracy	99.4%	(-.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	99.4%	(/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64))
✓	accuracy	97.4%	(PI.f64)
✓	accuracy	99.7%	(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))))
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(/.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	97.4%	(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	97.4%	(PI.f64)
✓	accuracy	99.6%	(*.f64 f (PI.f64))
✓	accuracy	99.6%	(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
✓	accuracy	99.3%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
✓	accuracy	97.4%	(PI.f64)
✓	accuracy	99.5%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
✓	accuracy	99.5%	(/.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	97.4%	(PI.f64)

Results

178.0ms	246×	0	valid
105.0ms	7×	5	exit
7.0ms	1×	2	valid
5.0ms	1×	3	valid
2.0ms	1×	1	valid

Compiler

Compiled 421 to 49 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

ival-log: 75.0ms (44.8% of total)

ival-div: 32.0ms (19.1% of total)

ival-mult: 23.0ms (13.7% of total)

ival-tanh: 19.0ms (11.4% of total)

...c/correct-round.rkt:119:19: 5.0ms (3% of total)

backward-pass: 5.0ms (3% of total)

ival-sub: 3.0ms (1.8% of total)

ival-add: 3.0ms (1.8% of total)

ival-pi: 2.0ms (1.2% of total)

const: 1.0ms (0.6% of total)

series188.0ms (0.9%)

Counts

25 → 180

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

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

Calls

45 calls:

Time	Variable		Point	Expression
153.0ms	f	@	0	(/ (- (log 2) (log (* (PI) (* f 1/2)))) (/ (PI) -4))
16.0ms	f	@	-inf	(/ (- (log 2) (log (* (PI) (* f 1/2)))) (/ (PI) -4))
7.0ms	f	@	inf	(/ (- (log 2) (log (* (PI) (* f 1/2)))) (/ (PI) -4))
2.0ms	f	@	0	(/ (PI) (log (tanh (/ (PI) (/ 4 f)))))
1.0ms	f	@	0	(- (/ (/ (log 2) (PI)) -1/4) (/ (/ (log (* (PI) (* f 1/2))) (PI)) -1/4))

rewrite475.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

5338×	`/-lowering-/.f32`
5338×	`/-lowering-/.f64`
4104×	`-lowering-.f32`
4104×	`-lowering-.f64`
1310×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	173
1	225	156
2	1512	156
0	8363	156

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 2102

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

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

simplify253.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

3616×	`-lowering-.f32`
3616×	`-lowering-.f64`
2328×	`+-lowering-+.f64`
2328×	`+-lowering-+.f32`
1458×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	3072
1	772	2694
2	3264	2396
0	9264	2396

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

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)))))
(+ (* -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))))))
(+ (* 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))))))
(+ (* 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))))))
(/ (PI) (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 (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(/ (PI) (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 (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(/ (PI) (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 (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(/ (PI) (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 (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(+ (log f) (log (* 1/4 (PI))))
(+ (log f) (+ (log (* 1/4 (PI))) (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI)))))
(+ (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)))))))
(+ (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)))))))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))
(* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))
(* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))
(* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))
(* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))
(* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))
(* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))
(* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(+ (log (/ 1 f)) (log (/ 4 (PI))))
(+ (log (/ 1 f)) (log (/ 4 (PI))))
(+ (log (/ 1 f)) (log (/ 4 (PI))))
(+ (log (/ 1 f)) (log (/ 4 (PI))))
(+ (log (/ -4 (PI))) (log (/ -1 f)))
(+ (log (/ -4 (PI))) (log (/ -1 f)))
(+ (log (/ -4 (PI))) (log (/ -1 f)))
(+ (log (/ -4 (PI))) (log (/ -1 f)))
(* -4 (/ (- (log 2) (+ (log f) (log (* 1/2 (PI))))) (PI)))
(* -4 (/ (- (log 2) (+ (log f) (log (* 1/2 (PI))))) (PI)))
(* -4 (/ (- (log 2) (+ (log f) (log (* 1/2 (PI))))) (PI)))
(* -4 (/ (- (log 2) (+ (log f) (log (* 1/2 (PI))))) (PI)))
(* -4 (/ (- (log 2) (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f))))) (PI)))
(* -4 (/ (- (log 2) (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f))))) (PI)))
(* -4 (/ (- (log 2) (+ (log (* 1/2 (PI))) (* -1 (log (/ 1 f))))) (PI)))
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Outputs
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(/.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))

eval710.0ms (3.3%)

Compiler: Compiled 70488 to 8171 computations (88.4% saved)

prune229.0ms (1.1%)

Pruning

18 alts after pruning (14 fresh and 4 done)

	Pruned	Kept	Total
New	2870	10	2880
Fresh	9	4	13
Picked	2	3	5
Done	0	1	1
Total	2881	18	2899

Accuracy

99.7%

Counts

2899 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	10.9%	(/.f64 (/.f64 (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (.f64 f (PI.f64))))))) (log1p.f64 (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (.f64 f (PI.f64))))))) (PI.f64)) #s(literal 1/4 binary64))
▶	94.4%	(/.f64 (/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))) (PI.f64)) #s(literal 1/4 binary64))
▶	94.3%	(/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (PI.f64)) #s(literal 1/4 binary64))
✓	99.1%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
▶	98.9%	(/.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))))))
	94.3%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	95.0%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	98.9%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
	98.9%	(/.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)))
	94.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)))))
	94.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (PI.f64))))
✓	94.1%	(-.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)))
	94.3%	(-.f64 (/.f64 (log.f64 #s(literal 4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (*.f64 (PI.f64) f)) (/.f64 (PI.f64) #s(literal -4 binary64))))
▶	94.2%	(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -1 binary64)))
	93.8%	(.f64 (/.f64 #s(literal -4 binary64) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
	94.3%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
	94.2%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64))))
✓	94.2%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Compiler

Compiled 471 to 366 computations (22.3% saved)

simplify206.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (PI.f64))
✓	cost-diff	128	(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -1 binary64)))
✓	cost-diff	6464	(pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -1 binary64))
✓	cost-diff	0	(log.f64 f)
✓	cost-diff	0	(+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))
✓	cost-diff	0	(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))) (PI.f64))
✓	cost-diff	0	(/.f64 (/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))) (PI.f64)) #s(literal 1/4 binary64))
✓	cost-diff	0	(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) f)))) f)
✓	cost-diff	0	(log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) f)))) f))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
✓	cost-diff	0	(log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (PI.f64))
✓	cost-diff	0	(/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (PI.f64)) #s(literal 1/4 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	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 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))

Rules

2420×	`sum3-define`
2050×	`-lowering-.f32`
2050×	`-lowering-.f64`
1402×	`fma-lowering-fma.f32`
1402×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	267
1	88	252
2	192	247
3	349	247
4	673	247
5	1241	247
6	2265	247
7	3999	247
8	5831	247
0	8152	247

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ 4 (PI)) (/ 1 (log (tanh (/ (PI) (/ 4 f))))))
(/ 4 (PI))
4
(PI)
(/ 1 (log (tanh (/ (PI) (/ 4 f)))))
1
(log (tanh (/ (PI) (/ 4 f))))
(tanh (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(/ 4 f)
f
(/ (/ (log (/ (PI) (/ 4 f))) (PI)) 1/4)
(/ (log (/ (PI) (/ 4 f))) (PI))
(log (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(PI)
(/ 4 f)
4
f
1/4
(/ (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f)) (/ (PI) -4))
(log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f))
(/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f)
(+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f))))
(/ 2 (* (PI) 1/2))
2
(* (PI) 1/2)
(PI)
1/2
(* f (* (PI) (* 1/12 f)))
f
(* (PI) (* 1/12 f))
(* 1/12 f)
1/12
(/ (PI) -4)
-4
(/ (/ (+ (log f) (log (* 1/4 (PI)))) (PI)) 1/4)
(/ (+ (log f) (log (* 1/4 (PI)))) (PI))
(+ (log f) (log (* 1/4 (PI))))
(log f)
f
(log (* 1/4 (PI)))
(* 1/4 (PI))
1/4
(PI)
(* (/ 1 (PI)) (pow (/ 1/4 (log (/ (PI) (/ 4 f)))) -1))
(/ 1 (PI))
1
(PI)
(pow (/ 1/4 (log (/ (PI) (/ 4 f)))) -1)
(/ 1/4 (log (/ (PI) (/ 4 f))))
1/4
(log (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(/ 4 f)
4
f
-1

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

localize384.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -1 binary64))
✓	accuracy	99.5%	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
✓	accuracy	99.3%	(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -1 binary64)))
✓	accuracy	97.4%	(PI.f64)
✓	accuracy	99.6%	(+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64))))
✓	accuracy	99.5%	(/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))) (PI.f64))
✓	accuracy	97.6%	(log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))
✓	accuracy	97.4%	(PI.f64)
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) f)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	99.4%	(*.f64 #s(literal 1/12 binary64) f)
✓	accuracy	99.4%	(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) f)))) f)
✓	accuracy	97.4%	(PI.f64)
✓	accuracy	100.0%	(log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))
✓	accuracy	99.5%	(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (PI.f64))
✓	accuracy	97.4%	(PI.f64)
✓	accuracy	99.6%	(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	99.5%	(/.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))))))
✓	accuracy	97.4%	(PI.f64)

Results

174.0ms	246×	0	valid
135.0ms	7×	5	exit
6.0ms	1×	3	valid
2.0ms	1×	2	valid
1.0ms	1×	1	valid

Compiler

Compiled 278 to 41 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 146.0ms

ival-log: 53.0ms (36.3% of total)

ival-div: 36.0ms (24.7% of total)

ival-tanh: 21.0ms (14.4% of total)

ival-mult: 11.0ms (7.5% of total)

ival-add: 7.0ms (4.8% of total)

ival-pow: 6.0ms (4.1% of total)

...c/correct-round.rkt:119:19: 5.0ms (3.4% of total)

backward-pass: 5.0ms (3.4% of total)

ival-pi: 2.0ms (1.4% of total)

const: 1.0ms (0.7% of total)

series88.0ms (0.4%)

Counts

22 → 204

Calls

Call 1

Inputs
#<alt (/ (/ 4 (PI)) (/ 1 (log (tanh (/ (PI) (/ 4 f))))))>
#<alt (/ 4 (PI))>
#<alt (PI)>
#<alt (/ 1 (log (tanh (/ (PI) (/ 4 f)))))>
#<alt (/ (/ (log (/ (PI) (/ 4 f))) (PI)) 1/4)>
#<alt (/ (log (/ (PI) (/ 4 f))) (PI))>
#<alt (log (/ (PI) (/ 4 f)))>
#<alt (/ (PI) (/ 4 f))>
#<alt (/ 2 (* (PI) 1/2))>
#<alt (/ (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f)) (/ (PI) -4))>
#<alt (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f))>
#<alt (/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f)>
#<alt (/ (/ (+ (log f) (log (* 1/4 (PI)))) (PI)) 1/4)>
#<alt (/ (+ (log f) (log (* 1/4 (PI)))) (PI))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (log f)>
#<alt (pow (/ 1/4 (log (/ (PI) (/ 4 f)))) -1)>
#<alt (* (/ 1 (PI)) (pow (/ 1/4 (log (/ (PI) (/ 4 f)))) -1))>
#<alt (/ 1 (PI))>
#<alt (log (tanh (/ (PI) (/ 4 f))))>
#<alt (* 1/12 f)>
#<alt (log (* 1/4 (PI)))>

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))))))>
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#<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 (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>
#<alt (* 1/12 f)>

Calls

51 calls:

Time	Variable		Point	Expression
15.0ms	f	@	-inf	(/ (/ (log (/ (PI) (/ 4 f))) (PI)) 1/4)
15.0ms	f	@	0	(/ (/ (log (/ (PI) (/ 4 f))) (PI)) 1/4)
10.0ms	f	@	inf	(/ (/ (log (/ (PI) (/ 4 f))) (PI)) 1/4)
7.0ms	f	@	0	(/ 1 (log (tanh (/ (PI) (/ 4 f)))))
7.0ms	f	@	0	(/ (/ (+ (log f) (log (* 1/4 (PI)))) (PI)) 1/4)

rewrite392.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

5166×	`-lowering-.f32`
5166×	`-lowering-.f64`
4158×	`/-lowering-/.f32`
4158×	`/-lowering-/.f64`
1180×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	169
1	206	157
2	1263	154
0	8376	154

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1638

Calls

Call 1

Inputs
(/ (/ 4 (PI)) (/ 1 (log (tanh (/ (PI) (/ 4 f))))))
(/ 4 (PI))
(PI)
(/ 1 (log (tanh (/ (PI) (/ 4 f)))))
(/ (/ (log (/ (PI) (/ 4 f))) (PI)) 1/4)
(/ (log (/ (PI) (/ 4 f))) (PI))
(log (/ (PI) (/ 4 f)))
(/ (PI) (/ 4 f))
(/ 2 (* (PI) 1/2))
(/ (log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f)) (/ (PI) -4))
(log (/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f))
(/ (+ (/ 2 (* (PI) 1/2)) (* f (* (PI) (* 1/12 f)))) f)
(/ (/ (+ (log f) (log (* 1/4 (PI)))) (PI)) 1/4)
(/ (+ (log f) (log (* 1/4 (PI)))) (PI))
(+ (log f) (log (* 1/4 (PI))))
(log f)
(pow (/ 1/4 (log (/ (PI) (/ 4 f)))) -1)
(* (/ 1 (PI)) (pow (/ 1/4 (log (/ (PI) (/ 4 f)))) -1))
(/ 1 (PI))
(log (tanh (/ (PI) (/ 4 f))))
(* 1/12 f)
(log (* 1/4 (PI)))

Outputs
(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) (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 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log1p.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log1p.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 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))))
(neg.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(neg.f64 (/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(neg.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 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.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 #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 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (.f64 (PI.f64) #s(literal -1/2 binary64))))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (PI.f64) (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 #s(literal -1 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 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 #s(literal -2 binary64) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 #s(literal -2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (.f64 (PI.f64) #s(literal -1/2 binary64))))
(/.f64 #s(literal -2 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(/.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 (/.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 2 binary64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal -2 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal -2 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 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 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal -4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) #s(literal -1/4 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal -2 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (.f64 (PI.f64) #s(literal -1/2 binary64)))
(/.f64 (.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 1/2 binary64))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) #s(literal -1/2 binary64))
(/.f64 (.f64 (/.f64 #s(literal -2 binary64) (PI.f64)) #s(literal 1 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (*.f64 (/.f64 #s(literal -2 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1/2 binary64))
(/.f64 (*.f64 (/.f64 #s(literal -2 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) #s(literal 1/2 binary64))
(/.f64 (.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (cbrt.f64 (PI.f64)))
(/.f64 (.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal -1 binary64)) (.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (.f64 (cbrt.f64 (PI.f64)) #s(literal -1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (sqrt.f64 (PI.f64)))
(/.f64 (.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) #s(literal -1 binary64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(/.f64 (.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) (.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (cbrt.f64 (PI.f64))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))) (/.f64 (sqrt.f64 (PI.f64)) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 4 binary64)) (PI.f64))
(/.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -4 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -2 binary64)) (.f64 (PI.f64) #s(literal -1/2 binary64)))
(/.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/2 binary64))
(/.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (/.f64 #s(literal -2 binary64) (PI.f64))) #s(literal -1/2 binary64))
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(.f64 (/.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))))
(.f64 (/.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))) (/.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64)))
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(*.f64 (/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 (/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (/.f64 #s(literal -1 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))) #s(literal -1 binary64))
(*.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal -1 binary64)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(.f64 (.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)))
(.f64 (.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) #s(literal -2 binary64)) (/.f64 #s(literal -2 binary64) (PI.f64)))
(.f64 (.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64))
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(exp.f64 (*.f64 (log.f64 (PI.f64)) #s(literal -1 binary64)))
(exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 (PI.f64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (PI.f64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
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(/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal -1 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
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(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
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(pow.f64 (cbrt.f64 (PI.f64)) #s(literal -3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -1/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/3 binary64))
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(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (.f64 (pow.f64 (PI.f64) #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 (PI.f64) #s(literal -1/3 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (.f64 (pow.f64 (PI.f64) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal -1 binary64))
(log.f64 (tanh.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 1/2 binary64) (cosh.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))))) (neg.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))))
(+.f64 (log.f64 (expm1.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))))))
(+.f64 (log.f64 (expm1.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))) (neg.f64 (log1p.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f))))))
(+.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))))))
(+.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))) (neg.f64 (log1p.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))))
(exp.f64 (*.f64 (log.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.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) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(-.f64 (log.f64 (expm1.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))) (log1p.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))))
(-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))) (log1p.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))))
(-.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) (cosh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(-.f64 (log.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f))))) (log.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))))))
(-.f64 (log.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))))) (log.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))))))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 1 binary64)) (/.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 (log.f64 (expm1.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))) #s(literal 1 binary64)) (/.f64 (log1p.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) f)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))) #s(literal 1 binary64)) (/.f64 (log1p.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 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)))) #s(literal 1 binary64))
(/.f64 #s(literal -1 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))))) #s(literal -1 binary64))
(pow.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 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)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(*.f64 #s(literal -1 binary64) (pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal 1 binary64)))
(*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) #s(literal -1 binary64))
(*.f64 f #s(literal 1/12 binary64))
(*.f64 #s(literal 1/12 binary64) f)
(.f64 (.f64 f #s(literal 1/12 binary64)) #s(literal 1 binary64))
(log.f64 (/.f64 (PI.f64) #s(literal 4 binary64)))
(+.f64 (log.f64 #s(literal 1/4 binary64)) (log.f64 (PI.f64)))
(+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 1/4 binary64)))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 (PI.f64) #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)) #s(literal 4 binary64))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))) (+.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) (log.f64 #s(literal 1/4 binary64))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (log.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64))))
(+.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (+.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (log.f64 #s(literal 1/4 binary64))))
(+.f64 (log.f64 (-.f64 #s(literal 0 binary64) (PI.f64))) (log.f64 #s(literal -1/4 binary64)))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 (PI.f64) #s(literal -4 binary64))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (log.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 #s(literal 1/2 binary64)))
(+.f64 (log.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))
(+.f64 (log.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (PI.f64)))) (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))))
(+.f64 (+.f64 (log.f64 #s(literal 1/4 binary64)) #s(literal 0 binary64)) (log.f64 (PI.f64)))
(+.f64 (+.f64 (log.f64 #s(literal 1/4 binary64)) (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))
(+.f64 (+.f64 (log.f64 #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))))
(-.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))))
(-.f64 (log.f64 (-.f64 #s(literal 0 binary64) (PI.f64))) (log.f64 #s(literal -4 binary64)))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -4 binary64) (PI.f64))))
(-.f64 (log.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))
(-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64))) (log.f64 #s(literal -2 binary64)))
(fma.f64 #s(literal 1 binary64) (log.f64 (PI.f64)) (log.f64 #s(literal 1/4 binary64)))
(neg.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))))

simplify331.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

3552×	`-lowering-.f32`
3552×	`-lowering-.f64`
2134×	`+-lowering-+.f64`
2134×	`+-lowering-+.f32`
1524×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	3727
1	1103	3264
2	4460	2951
0	10378	2951

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))))))
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Outputs
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(+ (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)))))))))))
(+.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (.f64 f (.f64 f (+.f64 (.f64 f (.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 #s(literal 24 binary64) (+.f64 (+.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64)))) (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/192 binary64)))) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 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 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (PI.f64)) #s(literal -1/3072 binary64))))) (.f64 (+.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64)))) (.f64 #s(literal -1/128 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (.f64 (PI.f64) #s(literal 1/8 binary64))))) (PI.f64))) #s(literal 1/6 binary64))) (.f64 #s(literal 4 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/128 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (+.f64 (.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/32 binary64)) #s(literal -1/8 binary64)) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal -1/768 binary64)))) (PI.f64)))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log.f64 (/.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64))))) (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64)))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log.f64 (/.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64))))) (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64)))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log.f64 (/.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64))))) (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64)))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log.f64 (/.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64))))) (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64)))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log.f64 (/.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64))))) (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64)))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log.f64 (/.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64))))) (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64)))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log.f64 (/.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64))))) (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64)))))))
(log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log.f64 (/.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64))))) (+.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 (PI.f64) (.f64 f #s(literal -1/4 binary64)))))))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))
(* 1/12 f)
(*.f64 f #s(literal 1/12 binary64))

eval818.0ms (3.8%)

Compiler: Compiled 50237 to 6960 computations (86.1% saved)

prune366.0ms (1.7%)

Pruning

21 alts after pruning (16 fresh and 5 done)

	Pruned	Kept	Total
New	2838	13	2851
Fresh	6	3	9
Picked	3	2	5
Done	1	3	4
Total	2848	21	2869

Accuracy

99.7%

Counts

2869 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.3%	(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))))) (PI.f64)) #s(literal 1/4 binary64))
	94.3%	(/.f64 (/.f64 (-.f64 (log.f64 (*.f64 (PI.f64) f)) (log.f64 #s(literal 4 binary64))) (PI.f64)) #s(literal 1/4 binary64))
✓	94.4%	(/.f64 (/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))) (PI.f64)) #s(literal 1/4 binary64))
	95.0%	(/.f64 (/.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)) (PI.f64)) #s(literal -1/4 binary64))
	93.9%	(/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) #s(literal 1/4 binary64))
✓	94.3%	(/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (PI.f64)) #s(literal 1/4 binary64))
	94.3%	(/.f64 (/.f64 (log.f64 (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
✓	99.1%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
	10.9%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))) (log1p.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))))))
	94.1%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)))))
	94.4%	(/.f64 (-.f64 (/.f64 (log.f64 (PI.f64)) (PI.f64)) (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (PI.f64))) #s(literal 1/4 binary64))
	94.3%	(/.f64 (+.f64 (/.f64 (log.f64 (PI.f64)) (PI.f64)) (*.f64 (log.f64 (/.f64 f #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (PI.f64)))) #s(literal 1/4 binary64))
	1.6%	(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	94.2%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
✓	98.9%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
	94.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (PI.f64))))
	94.1%	(/.f64 #s(literal -1 binary64) (.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))))
	94.8%	(/.f64 #s(literal -4 binary64) (/.f64 (PI.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))))
	94.3%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
	94.2%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 binary64))))
✓	94.2%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Compiler

Compiled 1287 to 530 computations (58.8% saved)

regimes98.0ms (0.5%)

Counts

58 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))))
(/.f64 (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64)) #s(literal -1/4 binary64))
(/.f64 (/.f64 (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 #s(literal -1 binary64) (.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 (log.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 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f)))))
(/.f64 (/.f64 (log.f64 (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))))) (PI.f64)) #s(literal 1/4 binary64))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) f)))))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.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 (/.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)) (PI.f64)) #s(literal -1/4 binary64))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (PI.f64) (.f64 #s(literal 1/12 binary64) 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 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 (/.f64 (+.f64 (log.f64 f) (log.f64 (*.f64 #s(literal 1/4 binary64) (PI.f64)))) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 (/.f64 (-.f64 (log.f64 (*.f64 (PI.f64) f)) (log.f64 #s(literal 4 binary64))) (PI.f64)) #s(literal 1/4 binary64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) f))) (log.f64 #s(literal 1/2 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 4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (PI.f64)))
(/.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.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 (/.f64 (log.f64 (PI.f64)) (PI.f64)) (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (PI.f64))) #s(literal 1/4 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.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 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -4 binary64) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(-.f64 (/.f64 (log.f64 #s(literal 4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (*.f64 (PI.f64) f)) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (/.f64 (log.f64 f) (PI.f64)) #s(literal -1/4 binary64)))
(/.f64 (+.f64 (/.f64 (log.f64 (PI.f64)) (PI.f64)) (*.f64 (log.f64 (/.f64 f #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (PI.f64)))) #s(literal 1/4 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.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 (PI.f64) (/.f64 #s(literal 4 binary64) f))) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) #s(literal 1/4 binary64))
(-.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 (.f64 (PI.f64) #s(literal 1/2 binary64)) f))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
(-.f64 (/.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 16 binary64))) (/.f64 (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 f)) (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 16 binary64))))
(/.f64 (+.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 f (+.f64 (/.f64 #s(literal 0 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 f (.f64 #s(literal 8 binary64) (+.f64 (/.f64 (+.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/128 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/384 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64))))))) (.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 0 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))))))) f)) (log.f64 #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 (tanh.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 (/.f64 #s(literal -1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.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 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))) (log1p.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))))))
(/.f64 (/.f64 (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (.f64 f (PI.f64))))))) (log1p.f64 (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (.f64 f (PI.f64))))))) (PI.f64)) #s(literal 1/4 binary64))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (*.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.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 f (/.f64 #s(literal -4 binary64) (PI.f64)))))))) (*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))))
(fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 #s(literal -4 binary64) (PI.f64)) (neg.f64 (/.f64 (log.f64 (.f64 #s(literal -2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.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))))))))

Outputs
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))

Calls

6 calls:

18.0ms	(/.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)))))
17.0ms	f
16.0ms	(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)
15.0ms	(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))))))
14.0ms	(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))))))))

Results

Accuracy	Segments	Branch
99.1%	1	`f`
99.1%	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))))))))`
99.1%	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)))))))`
99.1%	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))))))`
99.1%	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)))))`
99.1%	1	`(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)`

Compiler

Compiled 144 to 60 computations (58.3% saved)

regimes9.0ms (0%)

Counts

23 → 1

Calls

Call 1

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

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
98.9%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes13.0ms (0.1%)

Counts

20 → 1

Calls

Call 1

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

Outputs
(/.f64 (/.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)) (PI.f64)) #s(literal -1/4 binary64))

Calls

1 calls:

11.0ms

Results

Accuracy	Segments	Branch
95.0%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
94.8%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
94.3%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
94.3%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -59.3b remaining (-1602.4%)

Threshold costs -59.3b (-1602.4%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
94.2%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	92
1	52	92

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) f))))))
(/.f64 (/.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)) (PI.f64)) #s(literal -1/4 binary64))
(/.f64 #s(literal -4 binary64) (/.f64 (PI.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 (/.f64 (log.f64 (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) f)))) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64)) #s(literal -1/4 binary64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

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

soundness3.8s (17.9%)

Rules

5434×	`/-lowering-/.f32`
5434×	`/-lowering-/.f64`
5338×	`/-lowering-/.f32`
5338×	`/-lowering-/.f64`
5166×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	173
1	225	156
2	1512	156
0	8363	156
0	237	3072
1	772	2694
2	3264	2396
0	9264	2396
0	227	3085
1	749	2697
2	3270	2597
0	8945	2597
0	44	241
1	246	215
2	1647	213
0	8230	213
0	28	200
1	150	95
2	786	92
3	4076	92
0	8383	92
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	5297	32
13	5531	32
14	5938	32
15	7040	32
0	8021	32
0	40	169
1	206	157
2	1263	154
0	8376	154

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 221 to 149 computations (32.6% saved)

preprocess45.0ms (0.2%)

Compiler: Compiled 262 to 118 computations (55% saved)

analyze287.0ms (1.3%)

sample6.4s (30.1%)

preprocess301.0ms (1.4%)

explain389.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify161.0ms (0.8%)

localize707.0ms (3.3%)

series502.0ms (2.3%)

rewrite375.0ms (1.8%)

simplify244.0ms (1.1%)

eval334.0ms (1.6%)

prune196.0ms (0.9%)

simplify191.0ms (0.9%)

localize307.0ms (1.4%)

series468.0ms (2.2%)

rewrite430.0ms (2%)

simplify324.0ms (1.5%)

eval406.0ms (1.9%)

prune274.0ms (1.3%)

simplify208.0ms (1%)

localize380.0ms (1.8%)

series188.0ms (0.9%)

rewrite475.0ms (2.2%)

simplify253.0ms (1.2%)

eval710.0ms (3.3%)

prune229.0ms (1.1%)

simplify206.0ms (1%)

localize384.0ms (1.8%)

series88.0ms (0.4%)

rewrite392.0ms (1.8%)

simplify331.0ms (1.5%)

eval818.0ms (3.8%)

prune366.0ms (1.7%)

regimes98.0ms (0.5%)

regimes9.0ms (0%)

regimes13.0ms (0.1%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes2.0ms (0%)

simplify8.0ms (0%)

soundness3.8s (17.9%)

preprocess45.0ms (0.2%)

end0.0ms (0%)

Profiling