Details

analyze1.2s (20.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample152.0ms (2.6%)

Algorithm

1×

intervals

Results

115.0ms	124×	body	2048	valid
17.0ms	63×	body	1024	valid
7.0ms	33×	body	512	valid
2.0ms	18×	body	256	valid
1.0ms	18×	body	128	valid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

694×	`div-sub_binary64`
602×	`neg-mul-1_binary64`
550×	`sub-neg_binary64`
311×	`associate-/r*_binary64`
286×	`distribute-neg-frac_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	30	21
2	71	21
3	195	21
4	504	21
5	1254	21
6	2437	21
7	3311	21
8	4638	21
9	4955	21

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

0.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.7b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

Compiler

Compiled 30 to 20 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.2b	(.f64 5 (.f64 v v))
0.7b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite83.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 71

Calls

3 calls:

7.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
4.0ms	(.f64 5 (.f64 v v))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

Compiler

Compiled 1582 to 991 computations (37.4% saved)

series49.0ms (0.8%)

Error

0.7b

Counts

3 → 12

Calls

3 calls:

7.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
7.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
5.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 333 to 284 computations (14.7% saved)

simplify106.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-l_binary64`
391×	`div-sub_binary64`
376×	`times-frac_binary64`
367×	`associate-r_binary64`
235×	`associate-/l*_binary64`

Counts

83 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1943
1	302	1799
2	973	1785
3	3884	1785
4	4989	1785
5	4926	1785

prune20.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	2	43

Error

0.7b

Counts

43 → 2

Alt Table

Status	Error	Program
	1.7b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))
▶	0.8b	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))

Compiler

Compiled 552 to 372 computations (32.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (*.f64 v v) (pow.f64 v 4))
0.0b	(.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))
0.7b	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 41

Calls

3 calls:

8.0ms	(.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))
4.0ms	(+.f64 (*.f64 v v) (pow.f64 v 4))
1.0ms	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))

Compiler

Compiled 845 to 563 computations (33.4% saved)

series35.0ms (0.6%)

Error

0.7b

Counts

3 → 15

Calls

3 calls:

13.0ms	(.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))
10.0ms	(+.f64 (*.f64 v v) (pow.f64 v 4))
7.0ms	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))

Compiler

Compiled 369 to 319 computations (13.6% saved)

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

739×	`difference-of-squares_binary64`
512×	`associate-l_binary64`
435×	`associate-r_binary64`
375×	`unswap-sqr_binary64`
197×	`cancel-sign-sub-inv_binary64`

Counts

56 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	957
1	188	842
2	558	836
3	2118	836
4	4012	836
5	6085	836

prune28.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	41	4	45

Error

0.7b

Counts

45 → 4

Alt Table

Status	Error	Program
	1.7b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))) (sqrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (*.f64 v v))) -1))))
	2.3b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))) (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1)))) (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
▶	1.7b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))
✓	0.8b	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))

Compiler

Compiled 812 to 570 computations (29.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.7b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
1.0b	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)
1.0b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

12×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`

Counts

4 → 71

Calls

4 calls:

4.0ms	(.f64 5 (.f64 v v))
2.0ms	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))
2.0ms	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

Compiler

Compiled 1688 to 1124 computations (33.4% saved)

series39.0ms (0.7%)

Error

0.7b

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)
7.0ms	(.f64 5 (.f64 v v))
6.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
6.0ms	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))

Compiler

Compiled 463 to 402 computations (13.2% saved)

simplify146.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

861×	`times-frac_binary64`
464×	`associate-l_binary64`
399×	`log-prod_binary64`
352×	`associate-r_binary64`
331×	`exp-prod_binary64`

Counts

83 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	2188
1	170	1889
2	459	1864
3	1691	1864
4	3618	1861
5	4880	1861
6	4991	1861
7	4873	1861

prune24.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	54	6	60

Error

0.7b

Counts

60 → 6

Alt Table

Status	Error	Program
	1.7b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))) (sqrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (*.f64 v v))) -1))))
	2.3b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))) (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1)))) (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
▶	1.7b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)) 3))
	2.2b	(cbrt.f64 (exp.f64 (.f64 3 (log.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))))
✓	0.8b	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))
	2.2b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) 2) (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3))

Compiler

Compiled 799 to 555 computations (30.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)
1.0b	(pow.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)) 3)
1.0b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))
1.0b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)) 3))

rewrite101.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

96×	`cbrt-prod_binary64`
48×	`cube-prod_binary64`
48×	`unpow-prod-down_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`

Counts

4 → 137

Calls

4 calls:

6.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)) 3))
4.0ms	(pow.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)) 3)
2.0ms	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))
2.0ms	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)

Compiler

Compiled 3309 to 2332 computations (29.5% saved)

series51.0ms (0.9%)

Error

0.7b

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)) 3)
18.0ms	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)
7.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)) 3))
6.0ms	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))

Compiler

Compiled 484 to 430 computations (11.2% saved)

simplify256.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

768×	`times-frac_binary64`
491×	`log-prod_binary64`
427×	`exp-prod_binary64`
396×	`associate-l_binary64`
381×	`cube-prod_binary64`

Counts

149 → 132

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	5785
1	125	4899
2	346	4835
3	1556	4835
4	3507	4829
5	4550	4829
6	4942	4829
7	4889	4829

prune24.0ms (0.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	132	6	138

Error

0.7b

Counts

138 → 6

Alt Table

Status	Error	Program
	1.7b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))) (sqrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (*.f64 v v))) -1))))
	2.3b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))) (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1)))) (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
	1.7b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3)) 3))
	2.2b	(cbrt.f64 (exp.f64 (.f64 3 (log.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))))
	0.8b	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))
	2.2b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) 2) (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3))

Compiler

Compiled 1000 to 677 computations (32.3% saved)

regimes239.0ms (4.1%)

Accuracy

Total 0.0b remaining (1.8%)

Threshold costs 0.0b (1.8%)

Compiler

Compiled 6598 to 4724 computations (28.4% saved)

simplify106.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`distribute-lft-neg-in_binary64`
3×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	26	27
2	33	27
3	40	27
4	45	27
5	48	27
6	49	27
7	46	27

end1.0ms (0%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

sample2.9s (49.3%)

Algorithm

1×

intervals

Results

1.5s	3990×	body	2048	valid
565.0ms	1998×	body	1024	valid
213.0ms	1011×	body	512	valid
83.0ms	514×	body	128	valid
63.0ms	487×	body	256	valid
0.0ms	7×	body	128	nan

Compiler

Compiled 197 to 145 computations (26.4% saved)

Details

analyze1.2s (20.9%)

sample152.0ms (2.6%)

simplify77.0ms (1.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite83.0ms (1.4%)

series49.0ms (0.8%)

simplify106.0ms (1.8%)

prune20.0ms (0.3%)

localize7.0ms (0.1%)

rewrite42.0ms (0.7%)

series35.0ms (0.6%)

simplify82.0ms (1.4%)

prune28.0ms (0.5%)

localize10.0ms (0.2%)

rewrite53.0ms (0.9%)

series39.0ms (0.7%)

simplify146.0ms (2.5%)

prune24.0ms (0.4%)

localize13.0ms (0.2%)

rewrite101.0ms (1.7%)

series51.0ms (0.9%)

simplify256.0ms (4.4%)

prune24.0ms (0.4%)

regimes239.0ms (4.1%)

simplify106.0ms (1.8%)

end1.0ms (0%)

sample2.9s (49.3%)

Profiling