Details

analyze161.0ms (5.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 11 to 11 computations (0% saved)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	40×	body	128	nan
0.0ms	10×	body	128	invalid

Compiler

Compiled 21 to 24 computations (-14.3% saved)

simplify95.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.4b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
0.2b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
0.3b	(*.f64 y (sqrt.f64 z))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_6579`
9×	`associate-r_binary64_6497`
8×	`add-cube-cbrt_binary64_6592` `*-un-lft-identity_binary64_6557`
7×	`add-cbrt-cube_binary64_6593` `pow1_binary64_6618` `add-exp-log_binary64_6595`
6×	`associate-l_binary64_6498`
5×	`add-log-exp_binary64_6596`
4×	`sqrt-prod_binary64_6573`
3×	`unswap-sqr_binary64_6525`
2×	`flip-+_binary64_6531` `-commutative_binary64_6488` `pow-prod-down_binary64_6628` `associate-r/_binary64_6499` `prod-exp_binary64_6606` `flip3-+_binary64_6560` `cbrt-unprod_binary64_6590`
1×	`distribute-lft-in_binary64_6506` `sum-log_binary64_6648` `+-commutative_binary64_6487` `distribute-rgt-in_binary64_6507`

Counts

3 → 55

Calls

3 calls:

6.0ms	(*.f64 y (sqrt.f64 z))
6.0ms	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
3.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

series100.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
29.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
28.0ms	(*.f64 y (sqrt.f64 z))

simplify44.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5079	852

prune62.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	10	65

Error

0.3b

Counts

65 → 10

Compiler

Compiled 1010 to 459 computations (54.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 z))
0.2b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64_6573`
25×	`add-sqr-sqrt_binary64_6579`
21×	`associate-r_binary64_6497`
15×	`add-cube-cbrt_binary64_6592` `pow1_binary64_6618` `*-un-lft-identity_binary64_6557`
13×	`add-cbrt-cube_binary64_6593` `add-exp-log_binary64_6595`
7×	`associate-l_binary64_6498`
5×	`pow-prod-down_binary64_6628` `prod-exp_binary64_6606` `cbrt-unprod_binary64_6590`
4×	`sqrt-pow1_binary64_6575` `unswap-sqr_binary64_6525` `add-log-exp_binary64_6596`
3×	`*-commutative_binary64_6488`
2×	`associate-*r/_binary64_6499` `pow1/2_binary64_6637` `rem-sqrt-square_binary64_6570`
1×	`flip-+_binary64_6531` `distribute-lft-in_binary64_6506` `flip3-+_binary64_6560` `distribute-rgt-in_binary64_6507`

Counts

4 → 91

Calls

4 calls:

10.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
6.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
5.0ms	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
2.0ms	(sqrt.f64 (sqrt.f64 z))

series169.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt.f64 (sqrt.f64 z))
43.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
38.0ms	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
35.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

simplify86.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4926	1229
1	4926	1229

prune94.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	102	11	113

Error

0.2b

Counts

113 → 11

Compiler

Compiled 1848 to 715 computations (61.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 z))
0.2b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_6579`
22×	`sqrt-prod_binary64_6573`
21×	`add-exp-log_binary64_6595`
19×	`associate-r_binary64_6497`
14×	`add-cube-cbrt_binary64_6592` `*-un-lft-identity_binary64_6557`
13×	`add-cbrt-cube_binary64_6593`
11×	`prod-exp_binary64_6606`
10×	`pow1_binary64_6618`
7×	`associate-l_binary64_6498`
5×	`cbrt-unprod_binary64_6590`
4×	`sqrt-pow1_binary64_6575` `unswap-sqr_binary64_6525` `add-log-exp_binary64_6596`
3×	`*-commutative_binary64_6488` `unpow-prod-down_binary64_6636`
2×	`pow-exp_binary64_6625` `pow-prod-down_binary64_6628` `associate-*r/_binary64_6499` `pow-to-exp_binary64_6626` `pow1/2_binary64_6637` `rem-sqrt-square_binary64_6570`
1×	`flip-+_binary64_6531` `distribute-lft-in_binary64_6506` `sqr-pow_binary64_6529` `flip3-+_binary64_6560` `distribute-rgt-in_binary64_6507`

Counts

4 → 91

Calls

4 calls:

8.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
6.0ms	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))))
2.0ms	(sqrt.f64 (sqrt.f64 z))

series212.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))))
56.0ms	(sqrt.f64 (sqrt.f64 z))
54.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))
44.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))

simplify78.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4945	1600
1	4945	1600

prune109.0ms (3.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	103	11	114

Error

0.2b

Counts

114 → 11

Compiler

Compiled 2060 to 1113 computations (46% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4)))
0.2b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))))
0.3b	(*.f64 y (pow.f64 z 1/4))
0.3b	(.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))

rewrite31.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64_6595`
25×	`prod-exp_binary64_6606`
18×	`add-sqr-sqrt_binary64_6579`
17×	`associate-r_binary64_6497`
13×	`add-cbrt-cube_binary64_6593`
11×	`add-cube-cbrt_binary64_6592` `*-un-lft-identity_binary64_6557`
8×	`pow-exp_binary64_6625` `pow-to-exp_binary64_6626`
7×	`associate-l_binary64_6498` `unpow-prod-down_binary64_6636`
6×	`pow1_binary64_6618` `add-log-exp_binary64_6596`
5×	`cbrt-unprod_binary64_6590`
4×	`unswap-sqr_binary64_6525`
3×	`*-commutative_binary64_6488` `sqr-pow_binary64_6529`
2×	`flip-+_binary64_6531` `associate-*r/_binary64_6499` `flip3-+_binary64_6560`
1×	`distribute-lft-in_binary64_6506` `pow-prod-down_binary64_6628` `sum-log_binary64_6648` `+-commutative_binary64_6487` `distribute-rgt-in_binary64_6507`

Counts

4 → 88

Calls

4 calls:

8.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))
6.0ms	(*.f64 y (pow.f64 z 1/4))
6.0ms	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))))
4.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4)))

series156.0ms (5%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(*.f64 y (pow.f64 z 1/4))
39.0ms	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))))
32.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4)))
30.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))

simplify58.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5661	1218

prune85.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	7	8
Picked	0	1	1
Done	1	1	2
Total	101	10	111

Error

0.0b

Counts

111 → 10

Compiler

Compiled 1533 to 860 computations (43.9% saved)

regimes394.0ms (12.6%)

Accuracy

Total 0.1b remaining (96.8%)

Threshold costs 0.1b (96.8%)

Compiler

Compiled 3670 to 2782 computations (24.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	15
1	14	15

end0.0ms (0%)

sample1.1s (33.8%)

Algorithm

1×

intervals

Results

309.0ms	8000×	body	128	valid
38.0ms	1038×	body	128	nan
15.0ms	396×	body	128	invalid

Compiler

Compiled 511 to 390 computations (23.7% saved)

Details

analyze161.0ms (5.1%)

sample20.0ms (0.6%)

simplify95.0ms (3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

rewrite18.0ms (0.6%)

series100.0ms (3.2%)

simplify44.0ms (1.4%)

prune62.0ms (2%)

localize9.0ms (0.3%)

rewrite30.0ms (1%)

series169.0ms (5.4%)

simplify86.0ms (2.7%)

prune94.0ms (3%)

localize11.0ms (0.4%)

rewrite32.0ms (1%)

series212.0ms (6.7%)

simplify78.0ms (2.5%)

prune109.0ms (3.5%)

localize10.0ms (0.3%)

rewrite31.0ms (1%)

series156.0ms (5%)

simplify58.0ms (1.8%)

prune85.0ms (2.7%)

regimes394.0ms (12.6%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (33.8%)

Profiling