Details

analyze1.3s (18.5%)

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)

sample82.0ms (1.2%)

Algorithm

1×

intervals

Results

45.0ms	127×	body	2048	valid
17.0ms	67×	body	1024	valid
5.0ms	28×	body	512	valid
2.0ms	17×	body	256	valid
1.0ms	17×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify81.0ms (1.2%)

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

prune5.0ms (0.1%)

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

0.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.6b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

Compiler

Compiled 30 to 20 computations (33.3% saved)

localize8.0ms (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))
0.6b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite69.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

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)

series26.0ms (0.4%)

Error

0.6b

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))
7.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 333 to 284 computations (14.7% saved)

simplify146.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-l_binary64`
392×	`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	148	1997
1	307	1853
2	978	1839
3	3889	1839
4	4980	1839
5	5000	1839
6	4978	1839

prune19.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.6b

Counts

43 → 1

Alt Table

Status	Error	Program
▶	0.6b	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1)))

Compiler

Compiled 522 to 352 computations (32.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1))
0.1b	(*.f64 (pow.f64 v 6) 125)
0.6b	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1)))
20.1b	(cbrt.f64 (*.f64 (pow.f64 v 6) 125))

rewrite192.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

54×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
28×	`difference-of-squares_binary64`
21×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

9.0ms	(/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1))
4.0ms	(*.f64 (pow.f64 v 6) 125)
3.0ms	(cbrt.f64 (*.f64 (pow.f64 v 6) 125))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1)))

Compiler

Compiled 2387 to 1859 computations (22.1% saved)

series42.0ms (0.6%)

Error

0.6b

Counts

4 → 15

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1))
9.0ms	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1)))
8.0ms	(cbrt.f64 (*.f64 (pow.f64 v 6) 125))
7.0ms	(*.f64 (pow.f64 v 6) 125)

Compiler

Compiled 537 to 452 computations (15.8% saved)

simplify126.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

355×	`div-sub_binary64`
348×	`sub-neg_binary64`
316×	`*-commutative_binary64`
217×	`distribute-rgt-in_binary64`
193×	`distribute-lft-in_binary64`

Counts

122 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3255
1	393	3097
2	1311	3074
3	3692	3074
4	4970	3074

prune65.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	3	107

Error

0.6b

Counts

107 → 3

Alt Table

Status	Error	Program
▶	1.6b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1)))))
	2.1b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))) (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))))
✓	0.6b	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1)))

Compiler

Compiled 1868 to 1437 computations (23.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))
1.0b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1)))))
20.1b	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
20.1b	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))

rewrite121.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

30×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
20×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 82

Calls

4 calls:

29.0ms	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1)))))
3.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
3.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))

Compiler

Compiled 3001 to 2324 computations (22.6% saved)

series45.0ms (0.7%)

Error

0.6b

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))
10.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
10.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
7.0ms	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1)))))

Compiler

Compiled 823 to 674 computations (18.1% saved)

simplify182.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

839×	`times-frac_binary64`
512×	`unswap-sqr_binary64`
362×	`div-sub_binary64`
216×	`associate-/r/_binary64`
172×	`associate-/l/_binary64`

Counts

94 → 66

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	77	2801
1	120	2589
2	288	2481
3	710	2313
4	1577	2309
5	4121	2309
6	4609	2305
7	4904	2305
8	4851	2305

prune31.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Error

0.6b

Counts

69 → 4

Alt Table

Status	Error	Program
✓	1.6b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1)))))
▶	2.1b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) 5/2) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1))))))
	3.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))))) (pow.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))) 4))
✓	0.6b	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1)))

Compiler

Compiled 1081 to 836 computations (22.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) 5/2) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1))))))
1.0b	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))
20.1b	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
20.1b	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))

rewrite119.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

32×	`add-sqr-sqrt_binary64`
25×	`cbrt-prod_binary64`
12×	`unswap-sqr_binary64`
12×	`unpow-prod-down_binary64`
11×	`*-un-lft-identity_binary64`

Counts

4 → 72

Calls

4 calls:

10.0ms	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) 5/2) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1))))))
3.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
3.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
1.0ms	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))

Compiler

Compiled 3552 to 2807 computations (21% saved)

series67.0ms (1%)

Error

0.6b

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))
12.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
11.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
7.0ms	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) 5/2) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1))))))

Compiler

Compiled 893 to 744 computations (16.7% saved)

simplify189.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

709×	`times-frac_binary64`
570×	`unswap-sqr_binary64`
356×	`associate-l_binary64`
316×	`div-sub_binary64`
308×	`associate-r_binary64`

Counts

84 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	4546
1	199	4376
2	499	4348
3	1362	4344
4	2329	4340
5	4512	4340
6	4897	4340

prune42.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	1	0	1
Picked	1	0	1
Done	1	1	2
Total	50	4	54

Error

0.6b

Counts

54 → 4

Alt Table

Status	Error	Program
	3.5b	(.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))) 5/2) (pow.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1))))) 7/2))
✓	0.6b	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 125))) (-.f64 (.f64 v v) 1)))
	1.6b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))))) (pow.f64 (sqrt.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))) 5/2)) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))))) (pow.f64 (sqrt.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1))))) 5/2)))
	2.5b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))) (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))) 5/2))) (sqrt.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))))) (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (*.f64 v v) 1)))) 5/2))))

Compiler

Compiled 1660 to 1303 computations (21.5% saved)

regimes209.0ms (3%)

Accuracy

Total 0.0b remaining (1.7%)

Threshold costs 0.0b (1.7%)

Compiler

Compiled 5873 to 4478 computations (23.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	21	23
2	25	23
3	27	23
4	28	23
5	26	23

end1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

sample3.7s (53.6%)

Algorithm

1×

intervals

Results

1.9s	3998×	body	2048	valid
686.0ms	2015×	body	1024	valid
248.0ms	980×	body	512	valid
83.0ms	493×	body	256	valid
47.0ms	512×	body	128	valid
1.0ms	2×	body	4096	valid
0.0ms	8×	body	128	nan

Compiler

Compiled 243 to 195 computations (19.8% saved)

Details

analyze1.3s (18.5%)

sample82.0ms (1.2%)

simplify81.0ms (1.2%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite69.0ms (1%)

series26.0ms (0.4%)

simplify146.0ms (2.1%)

prune19.0ms (0.3%)

localize12.0ms (0.2%)

rewrite192.0ms (2.8%)

series42.0ms (0.6%)

simplify126.0ms (1.8%)

prune65.0ms (1%)

localize14.0ms (0.2%)

rewrite121.0ms (1.8%)

series45.0ms (0.7%)

simplify182.0ms (2.7%)

prune31.0ms (0.5%)

localize20.0ms (0.3%)

rewrite119.0ms (1.7%)

series67.0ms (1%)

simplify189.0ms (2.8%)

prune42.0ms (0.6%)

regimes209.0ms (3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample3.7s (53.6%)

Profiling