Details

analyze220.0ms

Algorithm

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

sample20.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	12×	body	80	invalid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	82	11
1	82	11

prune3.0ms

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

localize7.0ms

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

Algorithm

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)))

series34.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4985	885
1	4985	885

prune106.0ms

Filtered

56 candidates to 76 candidates (-35.7%)

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

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)))

rewrite37.0ms

Algorithm

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:

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1.0 (.f64 z z)))) (sqrt.f64 (+.f64 1.0 (.f64 z z))))
31.0ms	(/.f64 (/.f64 1.0 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1.0 (.f64 z z)))) (sqrt.f64 (+.f64 1.0 (.f64 z z)))))
7.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 z z)))
8.0ms	(sqrt.f64 (+.f64 1.0 (*.f64 z z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4991	1716
1	4991	1716

prune139.0ms

Filtered

94 candidates to 129 candidates (-37.2%)

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

localize8.0ms

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)))

rewrite45.0ms

Algorithm

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:

11.0ms	(/.f64 1 (.f64 y (+.f64 1.0 (.f64 z z))))
21.0ms	(.f64 (/.f64 1.0 x) (/.f64 1 (.f64 y (+.f64 1.0 (*.f64 z z)))))
6.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

series50.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/.f64 1 (.f64 y (+.f64 1.0 (.f64 z z))))
23.0ms	(.f64 (/.f64 1.0 x) (/.f64 1 (.f64 y (+.f64 1.0 (*.f64 z z)))))
12.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

simplify77.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5263	1232

prune103.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

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

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

Algorithm

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)))

series48.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/.f64 1.0 (.f64 (.f64 y (+.f64 1.0 (*.f64 z z))) x))
15.0ms	(.f64 (.f64 y (+.f64 1.0 (*.f64 z z))) x)
12.0ms	(.f64 y (+.f64 1.0 (.f64 z z)))

simplify25.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5095	797

prune57.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

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

regimes449.0ms

Accuracy

0% (1.5b remaining)

Error of 6.4b against oracle of 4.9b and baseline of 6.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	19
1	14	19

end0.0ms

sample470.0ms

Algorithm

intervals

Results

280.0ms	8000×	body	80	valid
15.0ms	451×	body	80	invalid

Details

analyze220.0ms

sample20.0ms

simplify6.0ms

prune3.0ms

localize7.0ms

rewrite16.0ms

series34.0ms

simplify48.0ms

prune106.0ms

localize9.0ms

rewrite37.0ms

series59.0ms

simplify57.0ms

prune139.0ms

localize8.0ms

rewrite45.0ms

series50.0ms

simplify77.0ms

prune103.0ms

localize7.0ms

rewrite22.0ms

series48.0ms

simplify25.0ms

prune57.0ms

regimes449.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample470.0ms

Profiling