Metrics for VandenBroeck and Keller, Equation (20)

analyze292.0ms (1.5%)

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: 160.0ms

ival-div: 35.0ms (21.9% of total)

ival-exp: 34.0ms (21.3% of total)

ival-mult: 24.0ms (15% of total)

ival-log: 20.0ms (12.5% of total)

ival-neg: 17.0ms (10.6% of total)

ival-add: 9.0ms (5.6% of total)

ival-sub: 9.0ms (5.6% of total)

ival-pi: 8.0ms (5% of total)

const: 3.0ms (1.9% of total)

backward-pass: 1.0ms (0.6% of total)

sample6.3s (31.9%)

Results

2.8s	7692×	1	valid
2.2s	7060×	1	invalid
182.0ms	162×	2	valid
97.0ms	402×	0	valid
1.0ms	6×	0	unsamplable

Precisions

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

ival-exp: 1.1s (26.5% of total)

ival-div: 741.0ms (18.6% of total)

ival-mult: 417.0ms (10.5% of total)

ival-log: 399.0ms (10% of total)

backward-pass: 388.0ms (9.8% of total)

ival-neg: 363.0ms (9.1% of total)

ival-add: 209.0ms (5.3% of total)

ival-pi: 190.0ms (4.8% of total)

ival-sub: 167.0ms (4.2% of total)

const: 49.0ms (1.2% of total)

Bogosity

preprocess302.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	115
1	94	96
2	259	96
3	651	96
4	1406	96
5	2471	96
6	3785	96
7	4366	96
8	4932	96
9	5419	96
10	6095	72
11	7412	69
0	16	36
1	51	32
2	131	32
3	284	32
4	481	32
5	699	32
6	936	32
7	1243	32
8	1893	32
9	2337	32
10	3078	32
11	4771	32
12	5330	32
13	5594	32
14	6132	32
15	7538	32
0	8072	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 (+ -1 (sqrt (pow (fast-exp f) (PI))))) (recip (- 1 (pow (pow (fast-exp f) (PI)) -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 (+ -1 (pow (pow (fast-exp f) (PI)) -1/2))) (recip (- 1 (sqrt (pow (fast-exp f) (PI))))))) (/ -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 (+ -1 (pow (pow (fast-exp f) (PI)) -1/2))) (recip (- 1 (sqrt (pow (fast-exp f) (PI))))))))

explain419.0ms (2.1%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
249	-	1	(0.0068276794891182525)	`(-.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))))`
6	-	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)))))`
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)`
0	-	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	-	`(exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))`
0	-	0	-	`(exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))`

Results

307.0ms	486×	1	valid
15.0ms	12×	2	valid
3.0ms	14×	0	valid

Compiler

Compiled 434 to 50 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 149.0ms

ival-exp: 38.0ms (25.5% of total)

backward-pass: 30.0ms (20.1% of total)

ival-div: 22.0ms (14.7% of total)

ival-mult: 17.0ms (11.4% of total)

ival-log: 15.0ms (10.1% of total)

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

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

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

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

const: 2.0ms (1.3% of total)

eval0.0ms (0%)

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

prune5.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.6%	(/.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)))
▶	5.6%	(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

▶

5.6%

(/.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)))

▶

5.6%

(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)

simplify190.0ms (1%)

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

2270×	`sum3-define`
1910×	`fnmadd-define`
1774×	`fma-define`
1440×	`sum5-define`
1074×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	350
1	79	322
2	173	322
3	332	322
4	526	322
5	744	322
6	981	322
7	1269	322
8	1921	322
9	2360	322
10	3099	322
11	4792	322
12	5352	322
13	5616	322
14	6154	322
15	7564	322
0	8098	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 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/ 1 (/ (PI) 4))
(/.f64 #s(literal 4 binary64) (PI.f64))
1
#s(literal 1 binary64)
(/ (PI) 4)
(/.f64 (PI.f64) #s(literal 4 binary64))
(PI)
(PI.f64)
4
#s(literal 4 binary64)
(log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))
(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))))
(/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
(+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))
(+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(exp (* (/ (PI) 4) f))
(exp.f64 (*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64))))
(* (/ (PI) 4) f)
(*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))
f
(exp (neg (* (/ (PI) 4) f)))
(exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))
(neg (* (/ (PI) 4) f))
(/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64))
(- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))
(-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))))
(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))))
(/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
(+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))
(+.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(exp (/ (* (PI) f) 4))
(exp.f64 (*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64))))
(/ (* (PI) f) 4)
(*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))
(* (PI) f)
(*.f64 (PI.f64) f)
(PI)
(PI.f64)
f
4
#s(literal 4 binary64)
(exp (/ (* (PI) f) -4))
(exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))
(/ (* (PI) f) -4)
(/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))
(-.f64 (exp.f64 (.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))

localize318.0ms (1.6%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.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	97.3%	(/.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	9.9%	(-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
✓	accuracy	99.7%	(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)
✓	accuracy	99.3%	(.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	97.3%	(/.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	9.9%	(-.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

241.0ms	244×	1	valid
13.0ms	6×	2	valid
7.0ms	6×	0	valid

Compiler

Compiled 343 to 29 computations (91.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 152.0ms

ival-div: 46.0ms (30.3% of total)

ival-exp: 33.0ms (21.8% of total)

backward-pass: 19.0ms (12.5% of total)

ival-mult: 18.0ms (11.9% of total)

ival-log: 14.0ms (9.2% of total)

ival-neg: 7.0ms (4.6% of total)

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

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

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

const: 1.0ms (0.7% of total)

series228.0ms (1.2%)

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
80.0ms	f	@	-inf	(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
65.0ms	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))))))))
39.0ms	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))))))))
30.0ms	f	@	inf	(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
4.0ms	f	@	0	(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))

rewrite480.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4494×	`-lowering-.f32`
4494×	`-lowering-.f64`
4374×	`/-lowering-/.f32`
4374×	`/-lowering-/.f64`
1534×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	200
1	198	95
2	1513	92
0	8184	92

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 1012

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

simplify227.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	3085
1	763	2697
2	3301	2597
0	9043	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))))
(- (* 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))))
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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 (PI.f64) (.f64 #s(literal 1/4 binary64) f)))) (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) f)))) (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) f)))) (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) f)))) (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) f)))) (-.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) f))
(* f (- (* 1/4 (PI)) (* -1/4 (PI))))
(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
(* 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 (.f64 (PI.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 (.f64 f f) (.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/61440 binary64))) (.f64 (.f64 (PI.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 (.f64 f 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 (.f64 (PI.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 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (PI.f64) (.f64 #s(literal 1/4 binary64) 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 (1.7%)

Compiler: Compiled 63487 to 5066 computations (92% saved)

prune188.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	1459	15	1474
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	1461	15	1476

Accuracy

100.0%

Counts

1476 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.0%	(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (.f64 #s(literal 0 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.9%	(/.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))))
	96.6%	(/.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)))
	97.1%	(/.f64 (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.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)))
	96.9%	(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))))
	96.5%	(/.f64 (.f64 (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 3 binary64))) #s(literal -4 binary64)) (.f64 (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))) (PI.f64)))
	99.2%	(/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
	97.0%	(/.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)))
▶	96.6%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	99.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
▶	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
▶	96.9%	(-.f64 (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)) #s(literal -1/4 binary64)))
▶	99.2%	(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64))))
	99.3%	(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1 binary64)))
	96.4%	(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))

Compiler

Compiled 810 to 478 computations (41% saved)

simplify199.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

3274×	`-lowering-.f32`
3274×	`-lowering-.f64`
1938×	`/-lowering-/.f32`
1938×	`/-lowering-/.f64`
1464×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	327
1	99	327
2	222	321
3	414	321
4	782	320
5	1640	320
6	4105	320
0	8178	320

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize366.0ms (1.9%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(-.f64 (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)) #s(literal -1/4 binary64)))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	99.4%	(/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
✓	accuracy	98.1%	(PI.f64)
✓	accuracy	99.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64)))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.5%	(sqrt.f64 (PI.f64))
✓	accuracy	98.1%	(PI.f64)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
✓	accuracy	99.5%	(/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.1%	(PI.f64)
✓	accuracy	99.7%	(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	98.1%	(PI.f64)
✓	accuracy	100.0%	(tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
✓	accuracy	99.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.1%	(PI.f64)

Results

177.0ms	250×	0	valid
97.0ms	5×	5	exit
9.0ms	1×	4	valid

Compiler

Compiled 331 to 40 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 164.0ms

ival-log: 57.0ms (34.8% of total)

ival-div: 40.0ms (24.4% of total)

ival-sinh: 16.0ms (9.8% of total)

ival-tanh: 14.0ms (8.5% of total)

ival-cosh: 14.0ms (8.5% of total)

ival-mult: 9.0ms (5.5% of total)

ival-pow: 5.0ms (3.1% of total)

backward-pass: 3.0ms (1.8% of total)

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

const: 1.0ms (0.6% of total)

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

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

series306.0ms (1.6%)

Counts

21 → 204

Calls

Call 1

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

Calls

51 calls:

Time	Variable		Point	Expression
127.0ms	f	@	inf	(- (/ (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (PI)) -1/4) (/ (/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (PI)) -1/4))
41.0ms	f	@	-inf	(- (/ (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (PI)) -1/4) (/ (/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (PI)) -1/4))
30.0ms	f	@	inf	(/ (log (tanh (/ f (/ 4 (PI))))) (/ (PI) 4))
29.0ms	f	@	-inf	(/ (log (tanh (/ f (/ 4 (PI))))) (/ (PI) 4))
20.0ms	f	@	0	(/ (log (/ 2 (* (PI) (* f 1/2)))) (/ (PI) -4))

rewrite467.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4084×	`/-lowering-/.f32`
4084×	`/-lowering-/.f64`
3492×	`-lowering-.f32`
3492×	`-lowering-.f64`
1698×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	170
1	235	164
2	1936	163
0	8408	163

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1705

Calls

Call 1

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

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

simplify293.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

4666×	`-lowering-.f32`
4666×	`-lowering-.f64`
1858×	`+-lowering-+.f64`
1858×	`+-lowering-+.f32`
1818×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	6170
1	1362	5152
2	6067	5096
0	8306	5096

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

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

eval419.0ms (2.1%)

Compiler: Compiled 77746 to 6432 computations (91.7% saved)

prune310.0ms (1.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	2921	12	2933
Fresh	9	1	10
Picked	4	1	5
Done	0	0	0
Total	2934	14	2948

Accuracy

100.0%

Counts

2948 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.6%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64)) #s(literal -1/4 binary64))
▶	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64))))))
▶	96.5%	(/.f64 (-.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f)) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.6%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.5%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 f #s(literal 1/2 binary64)))) (log.f64 (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.5%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.5%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	97.0%	(/.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)))
	96.1%	(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
✓	99.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
	96.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64)))))
▶	99.2%	(/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 f (PI.f64)) #s(literal 4 binary64)))))))
	96.4%	(-.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)))
▶	96.4%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Compiler

Compiled 412 to 327 computations (20.6% saved)

simplify194.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

4050×	`-lowering-.f32`
4050×	`-lowering-.f64`
1864×	`fma-define`
1836×	`/-lowering-/.f32`
1836×	`/-lowering-/.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	406
1	137	343
2	354	327
3	1000	320
4	3223	279
5	7519	279
0	8065	279

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize349.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(-.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f)) (log.f64 #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(/.f64 (-.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f)) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	99.4%	(/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f)
✓	accuracy	98.1%	(PI.f64)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 f (PI.f64)) #s(literal 4 binary64)))))))
✓	accuracy	99.5%	(/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64)))))
✓	accuracy	99.5%	(.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 f (PI.f64)) #s(literal 4 binary64))))))
✓	accuracy	98.1%	(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	98.1%	(PI.f64)
✓	accuracy	99.7%	(*.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	98.1%	(PI.f64)
✓	accuracy	99.7%	(*.f64 f (PI.f64))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64)))))
✓	accuracy	99.5%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64))))))
✓	accuracy	98.1%	(PI.f64)

Results

180.0ms	250×	0	valid
65.0ms	5×	5	exit
6.0ms	1×	4	valid

Compiler

Compiled 420 to 48 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 123.0ms

ival-log: 38.0ms (31% of total)

ival-div: 30.0ms (24.5% of total)

ival-mult: 19.0ms (15.5% of total)

ival-tanh: 15.0ms (12.2% of total)

backward-pass: 9.0ms (7.3% of total)

...c/correct-round.rkt:119:19: 4.0ms (3.3% of total)

ival-add: 3.0ms (2.4% of total)

const: 1.0ms (0.8% of total)

ival-pi: 1.0ms (0.8% of total)

ival-sub: 1.0ms (0.8% of total)

series73.0ms (0.4%)

Counts

22 → 168

Calls

Call 1

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

Calls

42 calls:

Time	Variable		Point	Expression
35.0ms	f	@	0	(/ (- (log (/ (/ 2 (PI)) f)) (log 1/2)) (/ (PI) -4))
17.0ms	f	@	-inf	(/ (- (log (/ (/ 2 (PI)) f)) (log 1/2)) (/ (PI) -4))
7.0ms	f	@	inf	(/ (- (log (/ (/ 2 (PI)) f)) (log 1/2)) (/ (PI) -4))
2.0ms	f	@	0	(/ 1 (log (tanh (/ (* f (PI)) 4))))
2.0ms	f	@	0	(/ 1/4 (log (tanh (/ (* f (PI)) 4))))

rewrite375.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2960×	`-lowering-.f32`
2960×	`-lowering-.f64`
2726×	`/-lowering-/.f32`
2726×	`/-lowering-/.f64`
1992×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	168
1	253	151
2	1877	151
0	8195	151

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 867

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 (log.f64 (expm1.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) f)) #s(literal 4 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log1p.f64 (exp.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) f)) #s(literal 4 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f)))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log1p.f64 (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) f))))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64)))))) (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64)))))))
(neg.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))))))
(neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))
(/.f64 #s(literal 4 binary64) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))))))))
(/.f64 #s(literal 4 binary64) (neg.f64 (neg.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))))
(/.f64 #s(literal 4 binary64) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))))) (-.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 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal -4 binary64) (.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64)))))))
(/.f64 #s(literal -4 binary64) (neg.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))))))
(/.f64 #s(literal -4 binary64) (.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))))) (-.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 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.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 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))) #s(literal 4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))) #s(literal 1/4 binary64)) (PI.f64))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))
(/.f64 (neg.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (PI.f64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))))))
(/.f64 (.f64 #s(literal -4 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))))) (PI.f64))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))
(/.f64 (neg.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))) (/.f64 (PI.f64) #s(literal 4 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (PI.f64)))) (neg.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))))
(/.f64 (neg.f64 (.f64 #s(literal -4 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (neg.f64 (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1/4 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))))
(pow.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (tanh.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))))) #s(literal -1 binary64))
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(*.f64 #s(literal -1/96 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1/96 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1/96 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1/96 binary64)) #s(literal -1 binary64)))
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(+.f64 (.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64)) (PI.f64)) (.f64 #s(literal -2 binary64) f)) (.f64 f (.f64 (PI.f64) #s(literal 1/8 binary64))))
(-.f64 (/.f64 (.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/8 binary64))) (.f64 f (.f64 (PI.f64) #s(literal 1/8 binary64)))) (-.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/8 binary64))) (.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64)) (PI.f64)) (.f64 #s(literal -2 binary64) f)))) (/.f64 (.f64 (.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64)) (PI.f64)) (.f64 #s(literal -2 binary64) f)) (.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64)) (PI.f64)) (.f64 #s(literal -2 binary64) f))) (-.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/8 binary64))) (.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64)) (PI.f64)) (.f64 #s(literal -2 binary64) f)))))
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(fma.f64 f (/.f64 (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64)) (.f64 f (*.f64 (PI.f64) #s(literal 1/8 binary64))))
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(.f64 f (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))))
(.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/48 binary64))) (PI.f64))) f)

simplify199.0ms (1%)

Algorithm

1×	egg-herbie

Rules

2460×	`-lowering-.f32`
2460×	`-lowering-.f64`
1304×	`sum4-define`
1132×	`times-frac`
1086×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	4380
1	951	3668
2	4282	2956
0	10060	2956

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

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)))
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(- (+ (log (/ 1 f)) (log (/ 2 (PI)))) (log 1/2))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
(- (+ (log (/ -2 (PI))) (log (/ -1 f))) (log 1/2))
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(/ 2 (* f (PI)))
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(/ 2 (* f (PI)))
(/ 2 (* f (PI)))
(/ 2 (* f (PI)))
(* f (PI))
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(* f (PI))
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(* f (PI))
(* f (PI))
(* f (PI))
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(* f (+ (* -1/24 (PI)) (* 1/8 (PI))))

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

eval266.0ms (1.4%)

Compiler: Compiled 41784 to 6531 computations (84.4% saved)

prune179.0ms (0.9%)

Pruning

15 alts after pruning (10 fresh and 5 done)

	Pruned	Kept	Total
New	1628	6	1634
Fresh	4	4	8
Picked	1	4	5
Done	0	1	1
Total	1633	15	1648

Accuracy

100.0%

Counts

1648 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.6%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64)) #s(literal -1/4 binary64))
✓	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64))))))
✓	96.5%	(/.f64 (-.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f)) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.5%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (/.f64 f #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	96.5%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	97.0%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (.f64 f (PI.f64)) #s(literal 1/12 binary64)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	99.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
	96.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64)))))
✓	99.2%	(/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 f (PI.f64)) #s(literal 4 binary64)))))))
	96.4%	(-.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)))
	96.5%	(-.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))))
▶	96.0%	(.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)))))
	96.5%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
▶	96.4%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
✓	96.4%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Compiler

Compiled 355 to 279 computations (21.4% saved)

simplify167.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))
✓	cost-diff	0	(/.f64 #s(literal -4 binary64) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))
✓	cost-diff	0	(.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)))))
✓	cost-diff	6656	(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
✓	cost-diff	0	(log.f64 (*.f64 f (PI.f64)))
✓	cost-diff	0	(log.f64 #s(literal 4 binary64))
✓	cost-diff	0	(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64))))
✓	cost-diff	0	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	0	(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (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)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64))
✓	cost-diff	0	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (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 (.f64 f (PI.f64)) #s(literal 1/12 binary64)))) f)
✓	cost-diff	0	(log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (.f64 f (PI.f64)) #s(literal 1/12 binary64)))) 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 (.f64 f (PI.f64)) #s(literal 1/12 binary64)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))

Rules

1800×	`fnmadd-define`
1622×	`fmsub-define`
1544×	`fma-lowering-fma.f32`
1544×	`fma-lowering-fma.f64`
1468×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	240
1	84	223
2	152	218
3	254	218
4	411	218
5	657	218
6	1162	218
7	2218	218
8	5405	218
0	8024	218

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize248.0ms (1.3%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
✓	accuracy	99.3%	(.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)))))
✓	accuracy	98.4%	(.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))
✓	accuracy	98.4%	(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
✓	accuracy	100.0%	(log.f64 (*.f64 f (PI.f64)))
✓	accuracy	99.8%	(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64))))
✓	accuracy	99.7%	(*.f64 f (PI.f64))
✓	accuracy	99.5%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	100.0%	(log.f64 (/.f64 #s(literal 4 binary64) f))
✓	accuracy	99.5%	(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64)))
✓	accuracy	99.3%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
✓	accuracy	100.0%	(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
✓	accuracy	99.7%	(*.f64 f (PI.f64))
✓	accuracy	99.6%	(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64))
✓	accuracy	99.7%	(*.f64 f (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 (.f64 f (PI.f64)) #s(literal 1/12 binary64)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	99.4%	(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (.f64 f (PI.f64)) #s(literal 1/12 binary64)))) f)
✓	accuracy	99.3%	(.f64 (.f64 f (PI.f64)) #s(literal 1/12 binary64))

Results

168.0ms

256×

valid

Compiler

Compiled 257 to 38 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-div: 34.0ms (41.8% of total)

ival-log: 22.0ms (27% of total)

ival-mult: 13.0ms (16% of total)

...c/correct-round.rkt:119:19: 4.0ms (4.9% of total)

ival-sub: 3.0ms (3.7% of total)

ival-cbrt: 2.0ms (2.5% of total)

ival-pi: 1.0ms (1.2% of total)

ival-add: 1.0ms (1.2% of total)

const: 1.0ms (1.2% of total)

backward-pass: 0.0ms (0% of total)

series564.0ms (2.9%)

Counts

23 → 192

Calls

Call 1

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

Outputs
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* -1/12 (* (pow f 2) (PI))))>
#<alt (+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* -1/12 (PI)) (* 1/1152 (* (pow f 2) (pow (PI) 3))))))>
#<alt (+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* -1/12 (PI)) (* (pow f 2) (+ (* -1/82944 (* (pow f 2) (pow (PI) 5))) (* 1/1152 (pow (PI) 3)))))))>
#<alt (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI)))>
#<alt (- (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (* 192 (/ 1 (* (pow f 2) (pow (PI) 3)))))>
#<alt (- (+ (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (/ 4608 (* (pow f 4) (pow (PI) 5)))) (/ 192 (* (pow f 2) (pow (PI) 3))))>
#<alt (- (+ (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (* 4608 (/ 1 (* (pow f 4) (pow (PI) 5))))) (+ (* 147456 (/ 1 (* (pow f 6) (pow (PI) 7)))) (/ 192 (* (pow f 2) (pow (PI) 3)))))>
#<alt (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI)))>
#<alt (- (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (* 192 (/ 1 (* (pow f 2) (pow (PI) 3)))))>
#<alt (- (+ (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (/ 4608 (* (pow f 4) (pow (PI) 5)))) (/ 192 (* (pow f 2) (pow (PI) 3))))>
#<alt (- (+ (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (* 4608 (/ 1 (* (pow f 4) (pow (PI) 5))))) (+ (* 147456 (/ 1 (* (pow f 6) (pow (PI) 7)))) (/ 192 (* (pow f 2) (pow (PI) 3)))))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* 1/48 (* (pow f 2) (pow (PI) 2)))))>
#<alt (+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* (pow f 2) (+ (* -1/4608 (* (pow f 2) (pow (PI) 4))) (* 1/48 (pow (PI) 2))))))>
#<alt (+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* (pow f 2) (+ (* 1/48 (pow (PI) 2)) (* (pow f 2) (+ (* -1/4608 (pow (PI) 4)) (* 1/331776 (* (pow f 2) (pow (PI) 6)))))))))>
#<alt (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f))))>
#<alt (+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (* 48 (/ 1 (* (pow f 2) (pow (PI) 2))))))>
#<alt (- (+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (/ 48 (* (pow f 2) (pow (PI) 2))))) (/ 1152 (* (pow f 4) (pow (PI) 4))))>
#<alt (- (+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (+ (* 36864 (/ 1 (* (pow f 6) (pow (PI) 6)))) (/ 48 (* (pow f 2) (pow (PI) 2)))))) (* 1152 (/ 1 (* (pow f 4) (pow (PI) 4)))))>
#<alt (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f))))>
#<alt (+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (* 48 (/ 1 (* (pow f 2) (pow (PI) 2))))))>
#<alt (- (+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (/ 48 (* (pow f 2) (pow (PI) 2))))) (/ 1152 (* (pow f 4) (pow (PI) 4))))>
#<alt (- (+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (+ (* 36864 (/ 1 (* (pow f 6) (pow (PI) 6)))) (/ 48 (* (pow f 2) (pow (PI) 2)))))) (* 1152 (/ 1 (* (pow f 4) (pow (PI) 4)))))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)>
#<alt (/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)>
#<alt (/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)>
#<alt (* 1/12 (* f (PI)))>
#<alt (* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))>
#<alt (* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))>
#<alt (* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))>
#<alt (* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (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))) (PI))>
#<alt (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))>
#<alt (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))>
#<alt (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))>
#<alt (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))>
#<alt (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))>
#<alt (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))>
#<alt (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))>
#<alt (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))>
#<alt (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))>
#<alt (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))>
#<alt (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (* -4 (/ (- (+ (log 4) (* -1 (log f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log 4) (* -1 (log f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log 4) (* -1 (log f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log 4) (* -1 (log f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log 4) (log (/ 1 f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log 4) (log (/ 1 f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log 4) (log (/ 1 f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log 4) (log (/ 1 f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log -4) (log (/ -1 f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log -4) (log (/ -1 f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log -4) (log (/ -1 f))) (log (PI))) (PI)))>
#<alt (* -4 (/ (- (+ (log -4) (log (/ -1 f))) (log (PI))) (PI)))>
#<alt (- (+ (log 4) (* -1 (log f))) (log (PI)))>
#<alt (- (+ (log 4) (* -1 (log f))) (log (PI)))>
#<alt (- (+ (log 4) (* -1 (log f))) (log (PI)))>
#<alt (- (+ (log 4) (* -1 (log f))) (log (PI)))>
#<alt (- (+ (log 4) (log (/ 1 f))) (log (PI)))>
#<alt (- (+ (log 4) (log (/ 1 f))) (log (PI)))>
#<alt (- (+ (log 4) (log (/ 1 f))) (log (PI)))>
#<alt (- (+ (log 4) (log (/ 1 f))) (log (PI)))>
#<alt (- (+ (log -4) (log (/ -1 f))) (log (PI)))>
#<alt (- (+ (log -4) (log (/ -1 f))) (log (PI)))>
#<alt (- (+ (log -4) (log (/ -1 f))) (log (PI)))>
#<alt (- (+ (log -4) (log (/ -1 f))) (log (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log f) (log (PI)))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log f) (log (PI)))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log f) (log (PI)))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log f) (log (PI)))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f))))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f))))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f))))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f))))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))) (PI)))>
#<alt (* -4 (/ (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))) (PI)))>
#<alt (- (log 4) (+ (log f) (log (PI))))>
#<alt (- (log 4) (+ (log f) (log (PI))))>
#<alt (- (log 4) (+ (log f) (log (PI))))>
#<alt (- (log 4) (+ (log f) (log (PI))))>
#<alt (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f)))))>
#<alt (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f)))))>
#<alt (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f)))))>
#<alt (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f)))))>
#<alt (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f)))))>
#<alt (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f)))))>
#<alt (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f)))))>
#<alt (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f)))))>
#<alt (+ (log f) (log (PI)))>
#<alt (+ (log f) (log (PI)))>
#<alt (+ (log f) (log (PI)))>
#<alt (+ (log f) (log (PI)))>
#<alt (+ (log (PI)) (* -1 (log (/ 1 f))))>
#<alt (+ (log (PI)) (* -1 (log (/ 1 f))))>
#<alt (+ (log (PI)) (* -1 (log (/ 1 f))))>
#<alt (+ (log (PI)) (* -1 (log (/ 1 f))))>
#<alt (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))>
#<alt (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))>
#<alt (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))>
#<alt (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))>
#<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 (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* f (PI)))>
#<alt (* 1/12 (* 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 (+ (log 4) (* -1 (log f)))>
#<alt (+ (log 4) (* -1 (log f)))>
#<alt (+ (log 4) (* -1 (log f)))>
#<alt (+ (log 4) (* -1 (log f)))>
#<alt (+ (log 4) (log (/ 1 f)))>
#<alt (+ (log 4) (log (/ 1 f)))>
#<alt (+ (log 4) (log (/ 1 f)))>
#<alt (+ (log 4) (log (/ 1 f)))>
#<alt (+ (log -4) (log (/ -1 f)))>
#<alt (+ (log -4) (log (/ -1 f)))>
#<alt (+ (log -4) (log (/ -1 f)))>
#<alt (+ (log -4) (log (/ -1 f)))>

Calls

48 calls:

Time	Variable		Point	Expression
277.0ms	f	@	inf	(/ (- (log 4) (log (* f (PI)))) (/ (PI) -4))
189.0ms	f	@	-inf	(* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))
41.0ms	f	@	0	(* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))
16.0ms	f	@	0	(/ (- (log 4) (log (* f (PI)))) (/ (PI) -4))
15.0ms	f	@	-inf	(/ (- (log 4) (log (* f (PI)))) (/ (PI) -4))

rewrite592.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

4470×	`-lowering-.f32`
4470×	`-lowering-.f64`
4352×	`/-lowering-/.f32`
4352×	`/-lowering-/.f64`
1482×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	156
1	213	145
2	1769	142
0	8828	142

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 2064

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal -1/2 binary64))))
(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 2 binary64) (neg.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64))))
(/.f64 #s(literal -4 binary64) (-.f64 #s(literal 0 binary64) (PI.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 (/.f64 (PI.f64) #s(literal -4 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 #s(literal -2 binary64) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(/.f64 #s(literal -2 binary64) (neg.f64 (neg.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)))))
(/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (PI.f64)))
(.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 4 binary64))
(*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) #s(literal -4 binary64))
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (log.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 f) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (/.f64 (PI.f64) #s(literal 4 binary64))))
(-.f64 (/.f64 (log.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (-.f64 #s(literal 0 binary64) f)) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (/.f64 (log.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f)))) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 f) (PI.f64)) #s(literal -1/4 binary64)))
(neg.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (/.f64 (PI.f64) #s(literal 4 binary64))))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))))))
(/.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (PI.f64)) #s(literal -1/4 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))) #s(literal 1 binary64))))
(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) #s(literal -4 binary64)) (PI.f64))
(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) #s(literal 1 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (.f64 (log.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f)))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 f))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))))
(/.f64 (neg.f64 (.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) #s(literal -4 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (neg.f64 (.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) #s(literal 4 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (neg.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (PI.f64))) #s(literal 1/4 binary64))
(/.f64 (neg.f64 (.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) #s(literal 1 binary64))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(pow.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(.f64 #s(literal -4 binary64) (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (PI.f64)))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (/.f64 (PI.f64) #s(literal -4 binary64))))
(.f64 #s(literal -2 binary64) (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 (log.f64 (/.f64 f (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))))) (/.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 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) #s(literal -1/4 binary64)))
(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (PI.f64)) #s(literal -4 binary64))
(.f64 (.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) #s(literal 1 binary64)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (cbrt.f64 (PI.f64))) (/.f64 #s(literal -4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (cbrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -1/4 binary64))))
(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (cbrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -4 binary64))))
(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal -4 binary64) (cbrt.f64 (PI.f64))))
(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (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 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (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 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f))) f)) (sqrt.f64 (PI.f64))) (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64))))
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(*.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -4 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) #s(literal 4 binary64))
(.f64 (pow.f64 (PI.f64) #s(literal -1/3 binary64)) (pow.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/3 binary64)) (pow.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -4 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal -4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) (cbrt.f64 (PI.f64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal -1 binary64)) (pow.f64 (PI.f64) #s(literal -1/3 binary64)))
(.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 (PI.f64))) #s(literal -1 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)))
(exp.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (log.f64 (PI.f64))))
(cbrt.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))))
(cbrt.f64 (.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))
(pow.f64 (PI.f64) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 3/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 9 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 6 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) #s(literal 1/3 binary64))
(pow.f64 (.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64))
(.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))
(.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64))
(.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))
(.f64 (cbrt.f64 (PI.f64)) (pow.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4/3 binary64)))
(.f64 (cbrt.f64 (PI.f64)) (pow.f64 (pow.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4/3 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 7/3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 7/3 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 5/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) (pow.f64 (PI.f64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (pow.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 7/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4/3 binary64)) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 7/3 binary64)) #s(literal 1 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (PI.f64) (.f64 f #s(literal 1/12 binary64)))
(.f64 f (.f64 (PI.f64) #s(literal 1/12 binary64)))
(.f64 (.f64 (PI.f64) f) #s(literal 1/12 binary64))
(.f64 #s(literal 1/12 binary64) (.f64 (PI.f64) f))
(.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) f)
(.f64 (.f64 #s(literal 1/12 binary64) f) (PI.f64))
(*.f64 (PI.f64) f)
(*.f64 f (PI.f64))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) f))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) f))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) f))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) f))
(.f64 (.f64 f #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 f (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.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)))
(log.f64 (/.f64 #s(literal 4 binary64) f))
(+.f64 (log.f64 #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 f)))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 4 binary64) f)))
(+.f64 (log.f64 #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) f))))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 f)) (log.f64 #s(literal 4 binary64)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (neg.f64 (-.f64 #s(literal 0 binary64) f))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 f #s(literal 4 binary64))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 (/.f64 f #s(literal 4 binary64)) #s(literal 1 binary64))))
(-.f64 (log.f64 #s(literal -4 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) f)))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (/.f64 f #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 3 binary64)) (+.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))))) (/.f64 (pow.f64 (log.f64 f) #s(literal 3 binary64)) (+.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))))))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64)) (log.f64 (.f64 #s(literal 4 binary64) f))) (/.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (log.f64 (.f64 #s(literal 4 binary64) f))))
(neg.f64 (log.f64 (/.f64 f #s(literal 4 binary64))))
(neg.f64 (log.f64 (/.f64 (/.f64 f #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 f) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f)))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64)) (pow.f64 (log.f64 f) #s(literal 2 binary64))) (log.f64 (*.f64 #s(literal 4 binary64) f)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 f) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 f) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64)) (pow.f64 (log.f64 f) #s(literal 2 binary64)))) (neg.f64 (log.f64 (*.f64 #s(literal 4 binary64) f))))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 f #s(literal 4 binary64))))

simplify319.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

2214×	`-lowering-.f32`
2214×	`-lowering-.f64`
2040×	`fma-lowering-fma.f32`
2040×	`fma-lowering-fma.f64`
1840×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2117
1	601	1951
2	1780	1937
3	5067	1937
0	8053	1937

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* -1/12 (* (pow f 2) (PI))))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* -1/12 (PI)) (* 1/1152 (* (pow f 2) (pow (PI) 3))))))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* -1/12 (PI)) (* (pow f 2) (+ (* -1/82944 (* (pow f 2) (pow (PI) 5))) (* 1/1152 (pow (PI) 3)))))))
(* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI)))
(- (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (* 192 (/ 1 (* (pow f 2) (pow (PI) 3)))))
(- (+ (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (/ 4608 (* (pow f 4) (pow (PI) 5)))) (/ 192 (* (pow f 2) (pow (PI) 3))))
(- (+ (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (* 4608 (/ 1 (* (pow f 4) (pow (PI) 5))))) (+ (* 147456 (/ 1 (* (pow f 6) (pow (PI) 7)))) (/ 192 (* (pow f 2) (pow (PI) 3)))))
(* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI)))
(- (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (* 192 (/ 1 (* (pow f 2) (pow (PI) 3)))))
(- (+ (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (/ 4608 (* (pow f 4) (pow (PI) 5)))) (/ 192 (* (pow f 2) (pow (PI) 3))))
(- (+ (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (* 4608 (/ 1 (* (pow f 4) (pow (PI) 5))))) (+ (* 147456 (/ 1 (* (pow f 6) (pow (PI) 7)))) (/ 192 (* (pow f 2) (pow (PI) 3)))))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* 1/48 (* (pow f 2) (pow (PI) 2)))))
(+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* (pow f 2) (+ (* -1/4608 (* (pow f 2) (pow (PI) 4))) (* 1/48 (pow (PI) 2))))))
(+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* (pow f 2) (+ (* 1/48 (pow (PI) 2)) (* (pow f 2) (+ (* -1/4608 (pow (PI) 4)) (* 1/331776 (* (pow f 2) (pow (PI) 6)))))))))
(+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f))))
(+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (* 48 (/ 1 (* (pow f 2) (pow (PI) 2))))))
(- (+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (/ 48 (* (pow f 2) (pow (PI) 2))))) (/ 1152 (* (pow f 4) (pow (PI) 4))))
(- (+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (+ (* 36864 (/ 1 (* (pow f 6) (pow (PI) 6)))) (/ 48 (* (pow f 2) (pow (PI) 2)))))) (* 1152 (/ 1 (* (pow f 4) (pow (PI) 4)))))
(+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f))))
(+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (* 48 (/ 1 (* (pow f 2) (pow (PI) 2))))))
(- (+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (/ 48 (* (pow f 2) (pow (PI) 2))))) (/ 1152 (* (pow f 4) (pow (PI) 4))))
(- (+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (+ (* 36864 (/ 1 (* (pow f 6) (pow (PI) 6)))) (/ 48 (* (pow f 2) (pow (PI) 2)))))) (* 1152 (/ 1 (* (pow f 4) (pow (PI) 4)))))
(/ 4 (* f (PI)))
(/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)
(/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)
(/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)
(* 1/12 (* f (PI)))
(* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))
(* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))
(* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))
(* 1/12 (* f (PI)))
(* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (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))) (PI))
(/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))
(/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))
(/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))
(/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))
(/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))
(/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))
(/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))
(/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))
(/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))
(/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))
(/ (+ (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 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(* -4 (/ (- (+ (log 4) (* -1 (log f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log 4) (* -1 (log f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log 4) (* -1 (log f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log 4) (* -1 (log f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log 4) (log (/ 1 f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log 4) (log (/ 1 f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log 4) (log (/ 1 f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log 4) (log (/ 1 f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log -4) (log (/ -1 f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log -4) (log (/ -1 f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log -4) (log (/ -1 f))) (log (PI))) (PI)))
(* -4 (/ (- (+ (log -4) (log (/ -1 f))) (log (PI))) (PI)))
(- (+ (log 4) (* -1 (log f))) (log (PI)))
(- (+ (log 4) (* -1 (log f))) (log (PI)))
(- (+ (log 4) (* -1 (log f))) (log (PI)))
(- (+ (log 4) (* -1 (log f))) (log (PI)))
(- (+ (log 4) (log (/ 1 f))) (log (PI)))
(- (+ (log 4) (log (/ 1 f))) (log (PI)))
(- (+ (log 4) (log (/ 1 f))) (log (PI)))
(- (+ (log 4) (log (/ 1 f))) (log (PI)))
(- (+ (log -4) (log (/ -1 f))) (log (PI)))
(- (+ (log -4) (log (/ -1 f))) (log (PI)))
(- (+ (log -4) (log (/ -1 f))) (log (PI)))
(- (+ (log -4) (log (/ -1 f))) (log (PI)))
(* -4 (/ (- (log 4) (+ (log f) (log (PI)))) (PI)))
(* -4 (/ (- (log 4) (+ (log f) (log (PI)))) (PI)))
(* -4 (/ (- (log 4) (+ (log f) (log (PI)))) (PI)))
(* -4 (/ (- (log 4) (+ (log f) (log (PI)))) (PI)))
(* -4 (/ (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f))))) (PI)))
(* -4 (/ (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f))))) (PI)))
(* -4 (/ (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f))))) (PI)))
(* -4 (/ (- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f))))) (PI)))
(* -4 (/ (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))) (PI)))
(* -4 (/ (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))) (PI)))
(* -4 (/ (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))) (PI)))
(* -4 (/ (- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))) (PI)))
(- (log 4) (+ (log f) (log (PI))))
(- (log 4) (+ (log f) (log (PI))))
(- (log 4) (+ (log f) (log (PI))))
(- (log 4) (+ (log f) (log (PI))))
(- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f)))))
(- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f)))))
(- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f)))))
(- (log 4) (+ (log (PI)) (* -1 (log (/ 1 f)))))
(- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f)))))
(- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f)))))
(- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f)))))
(- (log 4) (+ (log (* -1 (PI))) (* -1 (log (/ -1 f)))))
(+ (log f) (log (PI)))
(+ (log f) (log (PI)))
(+ (log f) (log (PI)))
(+ (log f) (log (PI)))
(+ (log (PI)) (* -1 (log (/ 1 f))))
(+ (log (PI)) (* -1 (log (/ 1 f))))
(+ (log (PI)) (* -1 (log (/ 1 f))))
(+ (log (PI)) (* -1 (log (/ 1 f))))
(+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))
(+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))
(+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))
(+ (log (* -1 (PI))) (* -1 (log (/ -1 f))))
(* -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)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* 1/12 (* f (PI)))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(* f (PI))
(+ (log 4) (* -1 (log f)))
(+ (log 4) (* -1 (log f)))
(+ (log 4) (* -1 (log f)))
(+ (log 4) (* -1 (log f)))
(+ (log 4) (log (/ 1 f)))
(+ (log 4) (log (/ 1 f)))
(+ (log 4) (log (/ 1 f)))
(+ (log 4) (log (/ 1 f)))
(+ (log -4) (log (/ -1 f)))
(+ (log -4) (log (/ -1 f)))
(+ (log -4) (log (/ -1 f)))
(+ (log -4) (log (/ -1 f)))

Outputs
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* -1/12 (* (pow f 2) (PI))))
(+.f64 (.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64))) (.f64 f (.f64 #s(literal -1/12 binary64) (.f64 (PI.f64) f))))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* -1/12 (PI)) (* 1/1152 (* (pow f 2) (pow (PI) 3))))))
(+.f64 (.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64))) (.f64 (.f64 f f) (.f64 (PI.f64) (+.f64 #s(literal -1/12 binary64) (.f64 (.f64 (PI.f64) (.f64 f (.f64 f #s(literal 1/1152 binary64)))) (PI.f64))))))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* -1/12 (PI)) (* (pow f 2) (+ (* -1/82944 (* (pow f 2) (pow (PI) 5))) (* 1/1152 (pow (PI) 3)))))))
(+.f64 (.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64))) (.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) #s(literal -1/12 binary64)) (.f64 f (.f64 f (+.f64 (.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) (.f64 (.f64 f f) #s(literal -1/82944 binary64))) (.f64 (PI.f64) (.f64 #s(literal 1/1152 binary64) (.f64 (PI.f64) (PI.f64))))))))))
(* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI)))
(.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 1/12 binary64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(- (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (* 192 (/ 1 (* (pow f 2) (pow (PI) 3)))))
(+.f64 (.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 1/12 binary64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal -192 binary64) (.f64 f f)) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))))
(- (+ (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (/ 4608 (* (pow f 4) (pow (PI) 5)))) (/ 192 (* (pow f 2) (pow (PI) 3))))
(+.f64 (.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 1/12 binary64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64))) (+.f64 (/.f64 (/.f64 #s(literal 4608 binary64) (.f64 f (.f64 f (.f64 f f)))) (pow.f64 (PI.f64) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal -192 binary64) (.f64 f f)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))))
(- (+ (* -4 (/ (+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f)))) (PI))) (* 4608 (/ 1 (* (pow f 4) (pow (PI) 5))))) (+ (* 147456 (/ 1 (* (pow f 6) (pow (PI) 7)))) (/ 192 (* (pow f 2) (pow (PI) 3)))))
(+.f64 (+.f64 (.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 1/12 binary64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64))) (+.f64 (/.f64 (/.f64 #s(literal 4608 binary64) (.f64 f (.f64 f (.f64 f f)))) (pow.f64 (PI.f64) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal -192 binary64) (.f64 f f)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))) (/.f64 #s(literal -147456 binary64) (*.f64 (pow.f64 f #s(literal 6 binary64)) (pow.f64 (PI.f64) #s(literal 7 binary64)))))
(* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI)))
(.f64 (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -1/12 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (/.f64 #s(literal -4 binary64) (PI.f64)))
(- (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (* 192 (/ 1 (* (pow f 2) (pow (PI) 3)))))
(+.f64 (.f64 (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -1/12 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (/.f64 #s(literal -4 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal -192 binary64) (.f64 f f)) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))))
(- (+ (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (/ 4608 (* (pow f 4) (pow (PI) 5)))) (/ 192 (* (pow f 2) (pow (PI) 3))))
(+.f64 (.f64 (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -1/12 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (/.f64 #s(literal -4 binary64) (PI.f64))) (+.f64 (/.f64 (/.f64 #s(literal 4608 binary64) (.f64 f (.f64 f (.f64 f f)))) (pow.f64 (PI.f64) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal -192 binary64) (.f64 f f)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))))
(- (+ (* -4 (/ (+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f)))) (PI))) (* 4608 (/ 1 (* (pow f 4) (pow (PI) 5))))) (+ (* 147456 (/ 1 (* (pow f 6) (pow (PI) 7)))) (/ 192 (* (pow f 2) (pow (PI) 3)))))
(+.f64 (/.f64 (/.f64 #s(literal 4608 binary64) (.f64 f (.f64 f (.f64 f f)))) (pow.f64 (PI.f64) #s(literal 5 binary64))) (+.f64 (.f64 (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -1/12 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (/.f64 #s(literal -4 binary64) (PI.f64))) (-.f64 (/.f64 (/.f64 #s(literal -192 binary64) (.f64 f f)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (/.f64 (/.f64 #s(literal 147456 binary64) (pow.f64 f #s(literal 6 binary64))) (pow.f64 (PI.f64) #s(literal 7 binary64))))))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* 1/48 (* (pow f 2) (pow (PI) 2)))))
(+.f64 (.f64 #s(literal 1/48 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (.f64 f f)))) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* (pow f 2) (+ (* -1/4608 (* (pow f 2) (pow (PI) 4))) (* 1/48 (pow (PI) 2))))))
(+.f64 (.f64 (.f64 f f) (+.f64 (.f64 (pow.f64 (PI.f64) #s(literal 4 binary64)) (.f64 (.f64 f f) #s(literal -1/4608 binary64))) (.f64 #s(literal 1/48 binary64) (*.f64 (PI.f64) (PI.f64))))) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* (pow f 2) (+ (* 1/48 (pow (PI) 2)) (* (pow f 2) (+ (* -1/4608 (pow (PI) 4)) (* 1/331776 (* (pow f 2) (pow (PI) 6)))))))))
(+.f64 (.f64 (.f64 f f) (+.f64 (.f64 #s(literal 1/48 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 f f) (+.f64 (.f64 #s(literal -1/4608 binary64) (pow.f64 (PI.f64) #s(literal 4 binary64))) (.f64 f (.f64 f (.f64 #s(literal 1/331776 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))))))))) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(+ (log (* 1/12 (PI))) (* -1 (log (/ 1 f))))
(+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 1/12 binary64))) (log.f64 f))
(+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (* 48 (/ 1 (* (pow f 2) (pow (PI) 2))))))
(+.f64 (log.f64 (.f64 (PI.f64) #s(literal 1/12 binary64))) (+.f64 (log.f64 f) (/.f64 #s(literal 48 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (.f64 f f))))))
(- (+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (/ 48 (* (pow f 2) (pow (PI) 2))))) (/ 1152 (* (pow f 4) (pow (PI) 4))))
(+.f64 (/.f64 #s(literal 48 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (.f64 f f)))) (+.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 1/12 binary64))) (log.f64 f)) (/.f64 (/.f64 #s(literal -1152 binary64) (.f64 f (.f64 f (*.f64 f f)))) (pow.f64 (PI.f64) #s(literal 4 binary64)))))
(- (+ (log (* 1/12 (PI))) (+ (* -1 (log (/ 1 f))) (+ (* 36864 (/ 1 (* (pow f 6) (pow (PI) 6)))) (/ 48 (* (pow f 2) (pow (PI) 2)))))) (* 1152 (/ 1 (* (pow f 4) (pow (PI) 4)))))
(+.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 1/12 binary64))) (log.f64 f)) (+.f64 (+.f64 (/.f64 #s(literal 48 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (.f64 f f)))) (/.f64 (/.f64 #s(literal 36864 binary64) (pow.f64 f #s(literal 6 binary64))) (pow.f64 (PI.f64) #s(literal 6 binary64)))) (/.f64 (/.f64 #s(literal -1152 binary64) (.f64 f (.f64 f (*.f64 f f)))) (pow.f64 (PI.f64) #s(literal 4 binary64)))))
(+ (log (* -1/12 (PI))) (* -1 (log (/ -1 f))))
(-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -1/12 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f)))
(+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (* 48 (/ 1 (* (pow f 2) (pow (PI) 2))))))
(+.f64 (log.f64 (.f64 (PI.f64) #s(literal -1/12 binary64))) (-.f64 (/.f64 #s(literal 48 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (.f64 f f)))) (log.f64 (/.f64 #s(literal -1 binary64) f))))
(- (+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (/ 48 (* (pow f 2) (pow (PI) 2))))) (/ 1152 (* (pow f 4) (pow (PI) 4))))
(+.f64 (log.f64 (.f64 (PI.f64) #s(literal -1/12 binary64))) (-.f64 (/.f64 #s(literal 48 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (.f64 f f)))) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (/.f64 (/.f64 #s(literal 1152 binary64) (.f64 f (.f64 f (*.f64 f f)))) (pow.f64 (PI.f64) #s(literal 4 binary64))))))
(- (+ (log (* -1/12 (PI))) (+ (* -1 (log (/ -1 f))) (+ (* 36864 (/ 1 (* (pow f 6) (pow (PI) 6)))) (/ 48 (* (pow f 2) (pow (PI) 2)))))) (* 1152 (/ 1 (* (pow f 4) (pow (PI) 4)))))
(+.f64 (log.f64 (.f64 (PI.f64) #s(literal -1/12 binary64))) (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 36864 binary64) (pow.f64 f #s(literal 6 binary64))) (pow.f64 (PI.f64) #s(literal 6 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) f))) (+.f64 (/.f64 #s(literal 48 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (.f64 f f)))) (/.f64 (/.f64 #s(literal -1152 binary64) (.f64 f (.f64 f (*.f64 f f)))) (pow.f64 (PI.f64) #s(literal 4 binary64))))))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)
(/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 f (*.f64 f #s(literal 1/12 binary64))))) f)
(/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)
(/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 f (*.f64 f #s(literal 1/12 binary64))))) f)
(/ (+ (* 1/12 (* (pow f 2) (PI))) (* 4 (/ 1 (PI)))) f)
(/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 f (*.f64 f #s(literal 1/12 binary64))))) f)
(* 1/12 (* f (PI)))
(.f64 #s(literal 1/12 binary64) (.f64 (PI.f64) f))
(* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))
(.f64 f (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 f f)))))
(* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))
(.f64 f (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 f f)))))
(* f (+ (* 1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI))))))
(.f64 f (+.f64 (.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 f f)))))
(* 1/12 (* f (PI)))
(.f64 #s(literal 1/12 binary64) (.f64 (PI.f64) f))
(* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(-.f64 #s(literal 0 binary64) (.f64 f (+.f64 (.f64 (PI.f64) #s(literal -1/12 binary64)) (/.f64 #s(literal -4 binary64) (.f64 (PI.f64) (.f64 f f))))))
(* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(-.f64 #s(literal 0 binary64) (.f64 f (+.f64 (.f64 (PI.f64) #s(literal -1/12 binary64)) (/.f64 #s(literal -4 binary64) (.f64 (PI.f64) (.f64 f f))))))
(* -1 (* f (- (* -1/12 (PI)) (* 4 (/ 1 (* (pow f 2) (PI)))))))
(-.f64 #s(literal 0 binary64) (.f64 f (+.f64 (.f64 (PI.f64) #s(literal -1/12 binary64)) (/.f64 #s(literal -4 binary64) (.f64 (PI.f64) (.f64 f f))))))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))
(*.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))
(*.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))
(*.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))
(*.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))) (/.f64 #s(literal -4 binary64) (PI.f64)))
(* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))
(*.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))) (/.f64 #s(literal -4 binary64) (PI.f64)))
(/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (PI.f64))
(/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (PI.f64))
(/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (PI.f64))
(/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (PI.f64))
(/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (PI.f64))
(/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (PI.f64))
(/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (PI.f64))
(/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (PI.f64))
(/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))
(/.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))) (PI.f64))
(/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))
(/.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))) (PI.f64))
(/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))
(/.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))) (PI.f64))
(/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI))
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(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f))
(+ (log (/ 1 f)) (log (/ 4 (PI))))
(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f))
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eval474.0ms (2.4%)

Compiler: Compiled 71837 to 6018 computations (91.6% saved)

prune349.0ms (1.8%)

Pruning

18 alts after pruning (9 fresh and 9 done)

	Pruned	Kept	Total
New	3154	7	3161
Fresh	3	2	5
Picked	1	4	5
Done	0	5	5
Total	3158	18	3176

Accuracy

100.0%

Counts

3176 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.0%	(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (PI.f64)) #s(literal -1/4 binary64))
✓	96.6%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (PI.f64)) #s(literal -1/4 binary64))
✓	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64))))))
	96.6%	(/.f64 (-.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (PI.f64)) (/.f64 (log.f64 (PI.f64)) (PI.f64))) #s(literal -1/4 binary64))
	96.5%	(/.f64 (-.f64 (/.f64 (log.f64 #s(literal 4 binary64)) (PI.f64)) (/.f64 (log.f64 (*.f64 (PI.f64) f)) (PI.f64))) #s(literal -1/4 binary64))
✓	96.5%	(/.f64 (-.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f)) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	96.5%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	97.0%	(/.f64 (log.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal 4 binary64))) (.f64 (.f64 (.f64 (.f64 f f) (PI.f64)) (.f64 (.f64 f f) (PI.f64))) #s(literal 1/144 binary64))) (.f64 f (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) f)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	1.6%	(/.f64 (log.f64 (.f64 #s(literal 1/12 binary64) (.f64 (PI.f64) f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	99.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
	96.9%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))))
✓	99.2%	(/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 f (PI.f64)) #s(literal 4 binary64)))))))
	96.4%	(/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f))))
	96.4%	(-.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)))
✓	96.0%	(.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)))))
	96.5%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
✓	96.4%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
✓	96.4%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Compiler

Compiled 1099 to 452 computations (58.9% saved)

regimes104.0ms (0.5%)

Counts

42 → 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 (/.f64 #s(literal 4 binary64) (PI.f64)) f))))
(/.f64 (log.f64 (.f64 #s(literal 1/12 binary64) (.f64 (PI.f64) f))) (/.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 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64)))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))
(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (PI.f64)) #s(literal -1/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (.f64 f (PI.f64)) #s(literal 1/12 binary64)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal 4 binary64))) (.f64 (.f64 (.f64 (.f64 f f) (PI.f64)) (.f64 (.f64 f f) (PI.f64))) #s(literal 1/144 binary64))) (.f64 f (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) 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 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 (.f64 f (PI.f64)) #s(literal 4 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (/.f64 f #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 f #s(literal 1/2 binary64)))) (log.f64 (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f)) (log.f64 #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (/.f64 (log.f64 #s(literal 4 binary64)) (PI.f64)) (/.f64 (log.f64 (*.f64 (PI.f64) f)) (PI.f64))) #s(literal -1/4 binary64))
(/.f64 (-.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (PI.f64)) (/.f64 (log.f64 (PI.f64)) (PI.f64))) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 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 (/.f64 (log.f64 #s(literal 2 binary64)) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))) (PI.f64)) #s(literal -1/4 binary64)))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4 binary64))))
(/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.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 (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)) #s(literal -1/4 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))))
(/.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))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (.f64 #s(literal 0 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 3 binary64))) #s(literal -4 binary64)) (.f64 (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))) (PI.f64)))

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

Calls

6 calls:

25.0ms	(/.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)))))
22.0ms	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))
11.0ms	(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)
11.0ms	f
9.0ms	(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))))))

Results

Accuracy	Segments	Branch
99.5%	1	`f`
99.5%	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))))))))`
99.5%	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)))))))`
99.5%	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))))))`
99.5%	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)))))`
99.5%	1	`(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)`

Compiler

Compiled 144 to 60 computations (58.3% saved)

regimes5.0ms (0%)

Counts

14 → 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 (/.f64 #s(literal 4 binary64) (PI.f64)) f))))
(/.f64 (log.f64 (.f64 #s(literal 1/12 binary64) (.f64 (PI.f64) f))) (/.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 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64)))))
(/.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) (*.f64 f #s(literal 1/2 binary64)))))))
(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f)) (PI.f64)) #s(literal -1/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (*.f64 #s(literal 1/12 binary64) f))) f))))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 (.f64 f (PI.f64)) #s(literal 1/12 binary64)))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/96 binary64) (PI.f64)))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 (PI.f64) #s(literal 4 binary64))) (.f64 (.f64 (.f64 (.f64 f f) (PI.f64)) (.f64 (.f64 f f) (PI.f64))) #s(literal 1/144 binary64))) (.f64 f (-.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 (.f64 (PI.f64) f) (.f64 #s(literal 1/12 binary64) 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 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
97.0%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
96.6%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
96.4%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
96.4%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify47.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	59
1	36	59

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness3.5s (17.6%)

Rules

4494×	`-lowering-.f32`
4494×	`-lowering-.f64`
4470×	`-lowering-.f32`
4470×	`-lowering-.f64`
4374×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	227	3085
1	763	2697
2	3301	2597
0	9043	2597
0	16	36
1	51	32
2	131	32
3	284	32
4	481	32
5	699	32
6	936	32
7	1243	32
8	1893	32
9	2337	32
10	3078	32
11	4771	32
12	5330	32
13	5594	32
14	6132	32
15	7538	32
0	8072	32
0	39	170
1	235	164
2	1936	163
0	8408	163
0	37	156
1	213	145
2	1769	142
0	8828	142
0	28	200
1	198	95
2	1513	92
0	8184	92
0	272	4380
1	951	3668
2	4282	2956
0	10060	2956

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

Compiler

Compiled 114 to 75 computations (34.2% saved)

preprocess41.0ms (0.2%)

Compiler: Compiled 196 to 92 computations (53.1% saved)

analyze292.0ms (1.5%)

sample6.3s (31.9%)

preprocess302.0ms (1.5%)

explain419.0ms (2.1%)

eval0.0ms (0%)

prune5.0ms (0%)

simplify190.0ms (1%)

localize318.0ms (1.6%)

series228.0ms (1.2%)

rewrite480.0ms (2.5%)

simplify227.0ms (1.2%)

eval334.0ms (1.7%)

prune188.0ms (1%)

simplify199.0ms (1%)

localize366.0ms (1.9%)

series306.0ms (1.6%)

rewrite467.0ms (2.4%)

simplify293.0ms (1.5%)

eval419.0ms (2.1%)

prune310.0ms (1.6%)

simplify194.0ms (1%)

localize349.0ms (1.8%)

series73.0ms (0.4%)

rewrite375.0ms (1.9%)

simplify199.0ms (1%)

eval266.0ms (1.4%)

prune179.0ms (0.9%)

simplify167.0ms (0.9%)

localize248.0ms (1.3%)

series564.0ms (2.9%)

rewrite592.0ms (3%)

simplify319.0ms (1.6%)

eval474.0ms (2.4%)

prune349.0ms (1.8%)

regimes104.0ms (0.5%)

regimes5.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify47.0ms (0.2%)

soundness3.5s (17.6%)

preprocess41.0ms (0.2%)

end0.0ms (0%)

Profiling