Details

analyze240.0ms (9.9%)

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
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

sample18.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
0.0ms	12×	body	80	invalid

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	82	11
1	82	11

prune6.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 5.4b

Counts

2 → 1

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

2.3b	(/.f64 (/.f64 1.0 x) (.f64 y (+.f64 1.0 (.f64 z z))))
3.8b	(.f64 y (+.f64 1.0 (.f64 z z)))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow1_binary64` `associate-*r/_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64` `prod-exp_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

2 → 70

Calls

2 calls:

8.0ms	(/.f64 (/.f64 1.0 x) (.f64 y (+.f64 1.0 (.f64 z z))))
6.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

series36.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

23.0ms	(/.f64 (/.f64 1.0 x) (.f64 y (+.f64 1.0 (.f64 z z))))
13.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

simplify47.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4985	885
1	4985	885

prune125.0ms (5.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 4.8b

Counts

77 → 8

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 y (sqrt.f64 (+.f64 1.0 (.f64 z z)))) (sqrt.f64 (+.f64 1.0 (.f64 z z))))
2.3b	(/.f64 (/.f64 1.0 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1.0 (.f64 z z)))) (sqrt.f64 (+.f64 1.0 (.f64 z z)))))
14.4b	(sqrt.f64 (+.f64 1.0 (*.f64 z z)))
14.4b	(sqrt.f64 (+.f64 1.0 (*.f64 z z)))

rewrite36.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`sqrt-div_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`associate-*r/_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
13×	`associate-/l*_binary64`
11×	`pow1_binary64`
9×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `sqrt-prod_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `associate-*l/_binary64`
3×	`pow-prod-down_binary64` `div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-/l/_binary64` `associate-/r_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 117

Calls

4 calls:

14.0ms	(/.f64 (/.f64 1.0 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1.0 (.f64 z z)))) (sqrt.f64 (+.f64 1.0 (.f64 z z)))))
11.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1.0 (.f64 z z)))) (sqrt.f64 (+.f64 1.0 (.f64 z z))))
3.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 z z)))

series49.0ms (2%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (/.f64 1.0 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1.0 (.f64 z z)))) (sqrt.f64 (+.f64 1.0 (.f64 z z)))))
13.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1.0 (.f64 z z)))) (sqrt.f64 (+.f64 1.0 (.f64 z z))))
5.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 z z)))
5.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 z z)))

simplify59.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4991	1716
1	4991	1716

prune188.0ms (7.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	128	9	137

Merged error: 4.8b

Counts

137 → 9

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1 (.f64 y (+.f64 1.0 (.f64 z z))))
2.2b	(.f64 (/.f64 1.0 x) (/.f64 1 (.f64 y (+.f64 1.0 (*.f64 z z)))))
3.8b	(.f64 y (+.f64 1.0 (.f64 z z)))

rewrite29.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-exp-log_binary64`
31×	`add-cbrt-cube_binary64`
24×	`prod-exp_binary64`
23×	`add-sqr-sqrt_binary64`
19×	`div-exp_binary64`
16×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `times-frac_binary64`
12×	`associate-r_binary64`
10×	`pow1_binary64` `cbrt-unprod_binary64`
9×	`cbrt-undiv_binary64`
7×	`associate-*r/_binary64`
6×	`1-exp_binary64` `rec-exp_binary64`
4×	`associate-/r/_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`pow-flip_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

3 → 109

Calls

3 calls:

13.0ms	(.f64 (/.f64 1.0 x) (/.f64 1 (.f64 y (+.f64 1.0 (*.f64 z z)))))
6.0ms	(/.f64 1 (.f64 y (+.f64 1.0 (.f64 z z))))
6.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

series57.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

24.0ms	(.f64 (/.f64 1.0 x) (/.f64 1 (.f64 y (+.f64 1.0 (*.f64 z z)))))
19.0ms	(/.f64 1 (.f64 y (+.f64 1.0 (.f64 z z))))
14.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

simplify76.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5263	1232

prune149.0ms (6.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	118	9	127

Merged error: 4.8b

Counts

127 → 9

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 1.0 (.f64 (.f64 y (+.f64 1.0 (*.f64 z z))) x))
2.2b	(.f64 (.f64 y (+.f64 1.0 (*.f64 z z))) x)
3.8b	(.f64 y (+.f64 1.0 (.f64 z z)))

rewrite22.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64` `add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`associate-r_binary64` `associate-*r/_binary64`
4×	`pow-prod-down_binary64` `associate-l_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

3 → 67

Calls

3 calls:

8.0ms	(/.f64 1.0 (.f64 (.f64 y (+.f64 1.0 (*.f64 z z))) x))
7.0ms	(.f64 (.f64 y (+.f64 1.0 (*.f64 z z))) x)
6.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

series50.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

21.0ms	(/.f64 1.0 (.f64 (.f64 y (+.f64 1.0 (*.f64 z z))) x))
16.0ms	(.f64 (.f64 y (+.f64 1.0 (*.f64 z z))) x)
13.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

simplify26.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5095	797

prune92.0ms (3.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	76	9	85

Merged error: 4.8b

Counts

85 → 9

regimes490.0ms (20.3%)

Accuracy

Total 1.5b remaining (23.7%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	19
1	14	19

end0.0ms (0%)

sample558.0ms (23.2%)

Algorithm

1×

intervals

Results

340.0ms	8000×	body	80	valid
19.0ms	451×	body	80	invalid

Details

analyze240.0ms (9.9%)

sample18.0ms (0.8%)

simplify6.0ms (0.2%)

prune6.0ms (0.2%)

localize10.0ms (0.4%)

rewrite16.0ms (0.7%)

series36.0ms (1.5%)

simplify47.0ms (1.9%)

prune125.0ms (5.2%)

localize9.0ms (0.4%)

rewrite36.0ms (1.5%)

series49.0ms (2%)

simplify59.0ms (2.4%)

prune188.0ms (7.8%)

localize9.0ms (0.4%)

rewrite29.0ms (1.2%)

series57.0ms (2.3%)

simplify76.0ms (3.2%)

prune149.0ms (6.2%)

localize7.0ms (0.3%)

rewrite22.0ms (0.9%)

series50.0ms (2.1%)

simplify26.0ms (1.1%)

prune92.0ms (3.8%)

regimes490.0ms (20.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample558.0ms (23.2%)

Profiling