Details

analyze1.3s (5.2%)

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)

sample404.0ms (1.6%)

Algorithm

1×

intervals

Results

133.0ms	122×	body	1024	nan
82.0ms	121×	body	1024	valid
31.0ms	72×	body	512	nan
27.0ms	62×	body	512	valid
22.0ms	16×	body	2048	valid
12.0ms	33×	body	256	valid
10.0ms	36×	body	256	nan
4.0ms	24×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify44.0ms (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

prune4.0ms (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

61.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.3b	(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

▶

61.3b

(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)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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)))))))
✓	0.2b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	1.5b	(/.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)))))
✓	5.8b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))

series971.0ms (3.9%)

Counts

4 → 48

Calls

4 calls:

928.0ms	(.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)))))))
32.0ms	(/.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 (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)

rewrite87.0ms (0.4%)

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:

20.0ms	(.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)))))))
10.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
8.0ms	(/.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)))))
4.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))

simplify544.0ms (2.2%)

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

prune699.0ms (2.8%)

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

1.5b

Counts

603 → 8

Alt Table

Status	Error	Program
	3.1b	(neg.f64 (*.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))))
	2.0b	(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))))))))
	2.9b	(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 4 (/.f64 (log.f64 f) (PI.f64)))))
▶	1.9b	(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))))))))
	2.9b	(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)))))))
	61.3b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (neg.f64 (log.f64 (+.f64 (sqrt.f64 (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))))) (.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))))) (-.f64 (sqrt.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))))))))
	2.0b	(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))))))))
	61.3b	(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))))))) (+.f64 (sqrt.f64 (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))))) (.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)))))) (-.f64 (sqrt.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (sqrt.f64 (exp.f64 (neg.f64 (*.f64 f (/.f64 (PI.f64) 4)))))))))))

Compiler

Compiled 31312 to 23674 computations (24.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))
✓	1.5b	(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)))))
✓	1.8b	(/.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))))
✓	3.4b	(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 (14%)

Counts

4 → 48

Calls

4 calls:

1.4s	(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))
419.0ms	(/.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))))
401.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))

rewrite41.0ms (0.2%)

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:

10.0ms	(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	(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)))))
6.0ms	(/.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))))
3.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))

simplify225.0ms (0.9%)

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

prune664.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	275	2	277
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	277	8	285

Error

1.5b

Counts

285 → 8

Alt Table

Status	Error	Program
	3.1b	(neg.f64 (*.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))))
	2.0b	(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))))))))
	2.9b	(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)))))))
	61.3b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (neg.f64 (log.f64 (+.f64 (sqrt.f64 (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))))) (.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))))) (-.f64 (sqrt.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))))))))
▶	1.9b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (.f64 1/2 (pow.f64 (pow.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) 2) 1/3)))) (.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 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))))))))
	3.1b	(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)) (exp.f64 (log.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))))))))))
	2.9b	(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 4 (/.f64 (log.f64 f) (PI.f64)))))

Compiler

Compiled 22791 to 17460 computations (23.4% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (pow.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) 2) 1/3)
	1.5b	(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)))))
	1.8b	(/.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))))
✓	3.4b	(log.f64 (.f64 1/2 (pow.f64 (pow.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (*.f64 f (PI.f64))))) 2) 1/3)))

series1.5s (6.1%)

Counts

2 → 8

Calls

2 calls:

1.1s

(log.f64 (*.f64 1/2 (pow.f64 (pow.f64 (+.f64 (exp.f64 (*.f64 -1/4 (*.f64 f (PI.f64)))) (exp.f64 (*.f64 1/4 (*.f64 f (PI.f64))))) 2) 1/3)))

413.0ms

(pow.f64 (pow.f64 (+.f64 (exp.f64 (*.f64 -1/4 (*.f64 f (PI.f64)))) (exp.f64 (*.f64 1/4 (*.f64 f (PI.f64))))) 2) 1/3)

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`unpow-prod-down_binary64`
13×	`add-exp-log_binary64`
8×	`pow-exp_binary64`
7×	`*-un-lft-identity_binary64`
6×	`rem-log-exp_binary64`

Counts

2 → 45

Calls

2 calls:

7.0ms

(log.f64 (*.f64 1/2 (pow.f64 (pow.f64 (+.f64 (exp.f64 (*.f64 -1/4 (*.f64 f (PI.f64)))) (exp.f64 (*.f64 1/4 (*.f64 f (PI.f64))))) 2) 1/3)))

5.0ms

(pow.f64 (pow.f64 (+.f64 (exp.f64 (*.f64 -1/4 (*.f64 f (PI.f64)))) (exp.f64 (*.f64 1/4 (*.f64 f (PI.f64))))) 2) 1/3)

simplify89.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

566×	`associate-r_binary64`
562×	`associate-l_binary64`
394×	`distribute-rgt-neg-in_binary64`
391×	`fma-neg_binary64`
226×	`fma-def_binary64`

Counts

53 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1703
1	266	1548
2	726	1482
3	3237	1476
4	4906	1476
5	4937	1476

prune505.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	213	8	221

Error

1.5b

Counts

221 → 8

Alt Table

Status	Error	Program
	3.1b	(neg.f64 (*.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))))
	2.0b	(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))))))))
	2.9b	(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)))))))
	61.3b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (neg.f64 (log.f64 (+.f64 (sqrt.f64 (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))))) (.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))))) (-.f64 (sqrt.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))))))))
	3.1b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (.f64 1/2 (pow.f64 (pow.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) 2) 1/3)))) (.f64 (/.f64 4 (PI.f64)) (exp.f64 (log.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))))))))))
✓	1.9b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (.f64 1/2 (pow.f64 (pow.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) 2) 1/3)))) (.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 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))))))))
	2.9b	(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 4 (/.f64 (log.f64 f) (PI.f64)))))

Compiler

Compiled 14803 to 11046 computations (25.4% 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))))))
✓	1.5b	(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)))))
✓	1.9b	(/.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))))
✓	2.4b	(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))

series2.0s (8.1%)

Counts

4 → 48

Calls

4 calls:

776.0ms	(.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))))))
756.0ms	(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)))))
423.0ms	(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))
61.0ms	(/.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))))

rewrite62.0ms (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:

13.0ms	(.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))))))
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))))
6.0ms	(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)))))
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))

simplify338.0ms (1.4%)

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

prune653.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	297	2	299
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	301	6	307

Error

1.5b

Counts

307 → 6

Alt Table

Status	Error	Program
	3.1b	(neg.f64 (*.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))))
	2.0b	(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))))))))
	2.9b	(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)))))))
	2.0b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (+.f64 (neg.f64 (log.f64 (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))))))))
✓	1.9b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (.f64 1/2 (pow.f64 (pow.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) 2) 1/3)))) (.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))))))))
	2.9b	(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))))))))

Compiler

Compiled 21468 to 16554 computations (22.9% saved)

regimes1.8s (7.3%)

Accuracy

Total 0.4b remaining (21.9%)

Threshold costs 0.4b (21.9%)

Counts

198 → 1

Compiler

Compiled 63532 to 50444 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

end1.0ms (0%)

Compiler: Compiled 51 to 40 computations (21.6% saved)

sample9.2s (37.3%)

Algorithm

1×

intervals

Results

2.5s	3945×	body	1024	valid
2.4s	3739×	body	1024	nan
1.3s	514×	body	2048	valid
900.0ms	1894×	body	512	valid
839.0ms	1980×	body	512	nan
322.0ms	1019×	body	256	valid
305.0ms	998×	body	256	nan
105.0ms	628×	body	128	valid
0.0ms	3×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 329 to 257 computations (21.9% saved)

Details

analyze1.3s (5.2%)

sample404.0ms (1.6%)

simplify44.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series971.0ms (3.9%)

rewrite87.0ms (0.4%)

simplify544.0ms (2.2%)

prune699.0ms (2.8%)

localize21.0ms (0.1%)

series3.5s (14%)

rewrite41.0ms (0.2%)

simplify225.0ms (0.9%)

prune664.0ms (2.7%)

localize29.0ms (0.1%)

series1.5s (6.1%)

rewrite15.0ms (0.1%)

simplify89.0ms (0.4%)

prune505.0ms (2%)

localize20.0ms (0.1%)

series2.0s (8.1%)

rewrite62.0ms (0.2%)

simplify338.0ms (1.4%)

prune653.0ms (2.6%)

regimes1.8s (7.3%)

simplify6.0ms (0%)

end1.0ms (0%)

sample9.2s (37.3%)

Profiling