Details

analyze1.3s (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample11.1s (40.4%)

Results

3.5s	4038×	body	1024	invalid
3.4s	3986×	body	1024	valid
1.3s	2105×	body	512	valid
1.1s	2019×	body	512	invalid
677.0ms	434×	body	2048	valid
456.0ms	998×	body	256	valid
386.0ms	975×	body	256	invalid
167.0ms	733×	body	128	valid
4.0ms	4×	body	2048	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify47.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
569×	`fma-def_binary64`
365×	`div-sub_binary64`
240×	`associate-/r*_binary64`
202×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	295	55
4	736	55
5	1625	55
6	4003	55
7	5053	55

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

60.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))

Status

Error

Program

▶

60.8b

(neg.f64 (*.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))

Compiler

Compiled 146 to 112 computations (23.3% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f)))))))
✓	0.3b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	1.2b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
✓	4.7b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))

series690.0ms (2.5%)

Counts

4 → 48

Calls

4 calls:

647.0ms	(.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f)))))))
33.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
6.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))
3.0ms	(*.f64 (/.f64 (PI.f64) 4) f)

rewrite82.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`times-frac_binary64`
167×	`*-un-lft-identity_binary64`
146×	`add-sqr-sqrt_binary64`
93×	`add-cube-cbrt_binary64`
72×	`log-prod_binary64`

Counts

4 → 271

Calls

4 calls:

18.0ms	(.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f)))))))
7.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
7.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
4.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))

simplify437.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
369×	`associate-l_binary64`
368×	`associate-r_binary64`
294×	`fma-neg_binary64`
216×	`*-commutative_binary64`

Counts

319 → 428

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	500	20519
1	1185	18587
2	3851	18571
3	4975	18571
4	4993	18571

prune663.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	594	8	602
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	595	8	603

Error

1.2b

Counts

603 → 8

Alt Table

Status	Error	Program
	60.8b	(neg.f64 (log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (-.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (/.f64 4 (PI.f64)))))
	1.9b	(neg.f64 (-.f64 (fma.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)) (.f64 1/12 (.f64 f (.f64 f (PI.f64))))) (.f64 7/5760 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 f 4)))))
▶	1.6b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))))
	2.0b	(neg.f64 (-.f64 (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))) (+.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))))))
	1.7b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f)))))))
	1.8b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 1/2)) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.1b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))
	1.6b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))

Compiler

Compiled 31228 to 23608 computations (24.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))
✓	1.2b	(cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))
✓	1.5b	(/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))
✓	2.9b	(log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (*.f64 f (/.f64 (PI.f64) 4))))))) 2))

series3.5s (12.6%)

Counts

4 → 48

Calls

4 calls:

1.5s	(log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))
1.2s	(log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (*.f64 f (/.f64 (PI.f64) 4))))))) 2))
424.0ms	(/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))
410.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))

rewrite37.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
40×	`cbrt-prod_binary64`
39×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`

Counts

4 → 132

Calls

4 calls:

8.0ms	(log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (*.f64 f (/.f64 (PI.f64) 4))))))) 2))
7.0ms	(/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))
5.0ms	(log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))
3.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))

simplify222.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

475×	`fma-def_binary64`
273×	`associate-/l*_binary64`
263×	`log-div_binary64`
246×	`fma-neg_binary64`
242×	`cancel-sign-sub-inv_binary64`

Counts

180 → 213

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	9901
1	658	8878
2	1910	8526
3	4611	8494
4	4910	8494

prune711.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	274	3	277
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	275	10	285

Error

1.2b

Counts

285 → 10

Alt Table

Status	Error	Program
	60.8b	(neg.f64 (log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (-.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (/.f64 4 (PI.f64)))))
	1.9b	(neg.f64 (-.f64 (fma.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)) (.f64 1/12 (.f64 f (.f64 f (PI.f64))))) (.f64 7/5760 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 f 4)))))
	1.7b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f)))))))
	2.2b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) 2))) (.f64 (/.f64 4 (PI.f64)) (.f64 (sqrt.f64 (log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))))))
	1.6b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
▶	1.6b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) 2))) (.f64 (/.f64 4 (PI.f64)) (-.f64 (log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (log.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))))
	45.4b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (pow.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))) 3)))))))
	2.0b	(neg.f64 (-.f64 (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))) (+.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))))))
	1.8b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 1/2)) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.1b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))

Compiler

Compiled 23111 to 17708 computations (23.4% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))))
	1.2b	(cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))
✓	1.2b	(log.f64 (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))
	2.9b	(log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (*.f64 f (/.f64 (PI.f64) 4))))))) 2))

series1.3s (4.6%)

Counts

2 → 24

Calls

2 calls:

855.0ms	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))))
406.0ms	(log.f64 (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`log-prod_binary64`
7×	`*-un-lft-identity_binary64`
5×	`cbrt-prod_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))))
1.0ms	(log.f64 (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-neg_binary64`
278×	`unswap-sqr_binary64`
277×	`associate-r_binary64`
269×	`fma-def_binary64`
258×	`distribute-rgt-neg-in_binary64`

Counts

61 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1950
1	304	1778
2	751	1745
3	2559	1741
4	4623	1741
5	4924	1741

prune559.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	205	10	215

Error

1.2b

Counts

215 → 10

Alt Table

Status	Error	Program
	60.8b	(neg.f64 (log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (-.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (/.f64 4 (PI.f64)))))
	1.9b	(neg.f64 (-.f64 (fma.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)) (.f64 1/12 (.f64 f (.f64 f (PI.f64))))) (.f64 7/5760 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 f 4)))))
	1.7b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f)))))))
	2.2b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) 2))) (.f64 (/.f64 4 (PI.f64)) (.f64 (sqrt.f64 (log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))))))
▶	1.6b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
✓	1.6b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) 2))) (.f64 (/.f64 4 (PI.f64)) (-.f64 (log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (log.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))))
	45.4b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (pow.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))) 3)))))))
	2.0b	(neg.f64 (-.f64 (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))) (+.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))))))
	1.8b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 1/2)) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.1b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))

Compiler

Compiled 16742 to 12893 computations (23% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))
✓	1.0b	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))
✓	1.6b	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))
✓	1.9b	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))

series2.1s (7.5%)

Counts

4 → 48

Calls

4 calls:

792.0ms	(.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))
784.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))
418.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))
64.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))

rewrite63.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`times-frac_binary64`
121×	`*-un-lft-identity_binary64`
115×	`log-prod_binary64`
94×	`add-sqr-sqrt_binary64`
89×	`add-cube-cbrt_binary64`

Counts

4 → 228

Calls

4 calls:

10.0ms	(.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))
7.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))
6.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))
5.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))

simplify458.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1012×	`times-frac_binary64`
239×	`associate-r_binary64`
227×	`*-commutative_binary64`
216×	`associate-/l*_binary64`
215×	`fma-def_binary64`

Counts

276 → 299

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	540	17828
1	1342	16830
2	4299	16825
3	6217	16825

prune697.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	295	4	299
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	301	8	309

Error

1.2b

Counts

309 → 8

Alt Table

Status	Error	Program
	60.8b	(neg.f64 (log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (-.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (/.f64 4 (PI.f64)))))
	1.9b	(neg.f64 (-.f64 (fma.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)) (.f64 1/12 (.f64 f (.f64 f (PI.f64))))) (.f64 7/5760 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 f 4)))))
	2.1b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))
	1.6b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (+.f64 (log.f64 (/.f64 1 (sqrt.f64 2))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 2))))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.1b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (-.f64 (fma.f64 4 (/.f64 (log.f64 (.f64 4 (/.f64 (sqrt.f64 2) (PI.f64)))) (PI.f64)) (.f64 1/8 (/.f64 (.f64 f (.f64 f (PI.f64))) 2))) (fma.f64 4 (/.f64 (log.f64 f) (PI.f64)) (.f64 1/24 (.f64 f (.f64 f (PI.f64))))))))
	1.7b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (+.f64 (.f64 (neg.f64 (log.f64 (.f64 (cbrt.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))) (cbrt.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (/.f64 4 (PI.f64))) (.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))) (/.f64 4 (PI.f64))))))
	1.7b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (+.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (/.f64 4 (PI.f64))) (.f64 (log.f64 (/.f64 (sqrt.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4)))) (sqrt.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (/.f64 4 (PI.f64))))))
✓	1.6b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) 2))) (.f64 (/.f64 4 (PI.f64)) (-.f64 (log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (log.f64 (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))))

Compiler

Compiled 21638 to 16687 computations (22.9% saved)

regimes3.2s (11.6%)

Accuracy

Total 0.4b remaining (23.8%)

Threshold costs 0.4b (23.8%)

Counts

264 → 1

Compiler

Compiled 89166 to 70831 computations (20.6% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	89
1	41	89
2	72	87
3	94	87
4	108	87
5	114	87
6	115	87
7	114	87

end293.0ms (1.1%)

Compiler: Compiled 510 to 398 computations (22% saved)

Details

analyze1.3s (4.7%)

sample11.1s (40.4%)

simplify47.0ms (0.2%)

prune6.0ms (0%)

localize12.0ms (0%)

series690.0ms (2.5%)

rewrite82.0ms (0.3%)

simplify437.0ms (1.6%)

prune663.0ms (2.4%)

localize22.0ms (0.1%)

series3.5s (12.6%)

rewrite37.0ms (0.1%)

simplify222.0ms (0.8%)

prune711.0ms (2.6%)

localize23.0ms (0.1%)

series1.3s (4.6%)

rewrite7.0ms (0%)

simplify100.0ms (0.4%)

prune559.0ms (2%)

localize20.0ms (0.1%)

series2.1s (7.5%)

rewrite63.0ms (0.2%)

simplify458.0ms (1.7%)

prune697.0ms (2.5%)

regimes3.2s (11.6%)

simplify6.0ms (0%)

end293.0ms (1.1%)

Profiling