Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.2%	87.6%	0.2%	13
21.8%	77.8%	0.4%	14

sample35.0ms

Algorithm

intervals

Results

13.0ms	209×	body	80	valid
2.0ms	17×	body	640	valid
2.0ms	47×	body	80	invalid
2.0ms	9×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	11×	body	160	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4892	13
1	4892	13

prune4.0ms

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: 25.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y z) (-.f64 t x))
2.7b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
18.2b	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`flip3--_binary64` `flip--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/l/_binary64` `frac-times_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 79

Calls

3 calls:

10.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
13.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

series110.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
55.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
43.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	6037	1081

prune174.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	74	14	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	14	89

Merged error: 4.1b

Counts

89 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
1.3b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
8.5b	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
46×	`associate-r_binary64`
37×	`cbrt-prod_binary64`
27×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
18×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
17×	`associate-l_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `unswap-sqr_binary64`
5×	`frac-times_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
38.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
6.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt.f64 (-.f64 a z))
26.0ms	(cbrt.f64 (-.f64 a z))
67.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
60.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5292	2530

prune175.0ms

Filtered

107 candidates to 146 candidates (-36.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	4	9	13
Picked	0	1	1
Done	0	0	0
Total	145	15	160

Merged error: 3.9b

Counts

160 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
1.3b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
9.3b	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

124×	`cbrt-div_binary64`
58×	`add-exp-log_binary64`
38×	`add-cbrt-cube_binary64`
35×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
34×	`associate-/r/_binary64`
33×	`frac-times_binary64`
25×	`cbrt-unprod_binary64` `prod-exp_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64` `associate-*l/_binary64`
11×	`associate-*r/_binary64` `times-frac_binary64`
10×	`add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`pow1/3_binary64` `unswap-sqr_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 131

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 a z))
4.0ms	(cbrt.f64 (-.f64 a z))
50.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
5.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt.f64 (-.f64 a z))
25.0ms	(cbrt.f64 (-.f64 a z))
68.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
60.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5092	2605

prune171.0ms

Filtered

96 candidates to 143 candidates (-49.0%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	142	16	158

Merged error: 3.9b

Counts

158 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
2.4b	(.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
9.0b	(+.f64 x (.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac_binary64`
166×	`add-sqr-sqrt_binary64`
115×	`cbrt-prod_binary64`
103×	`*-un-lft-identity_binary64`
80×	`associate-l_binary64`
76×	`cbrt-div_binary64`
61×	`associate-r_binary64`
59×	`add-cube-cbrt_binary64`
42×	`associate-/r/_binary64`
36×	`add-exp-log_binary64`
33×	`flip3--_binary64` `flip--_binary64`
22×	`add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
21×	`frac-times_binary64`
20×	`unswap-sqr_binary64`
14×	`cbrt-undiv_binary64` `div-exp_binary64`
11×	`associate-r/_binary64` `associate-l/_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `div-inv_binary64`
2×	`pow1/3_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 230

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
97.0ms	(.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
5.0ms	(+.f64 x (.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (-.f64 a z))
27.0ms	(cbrt.f64 (-.f64 a z))
65.0ms	(.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
62.0ms	(+.f64 x (.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5285	7659

prune213.0ms

Filtered

194 candidates to 242 candidates (-24.7%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	240	2	242
Fresh	1	12	13
Picked	0	1	1
Done	0	2	2
Total	241	17	258

Merged error: 3.9b

Counts

258 → 17

regimes683.0ms

Accuracy

9.5% (8.2b remaining)

Error of 11.7b against oracle of 3.4b and baseline of 12.5b

bsearch95.0ms

Steps

Iters	Range		Point
10	2.452270815779643e-48	2.5586763676582057e-34	1.886559025907838e-47
4	3.873685569259841e-136	6.666512897973093e-136	4.83371996350502e-136
9	2.437436983854017e-260	9.035080369347949e-254	7.901198986015583e-256
8	-1.213165485496787e-137	-1.4605853938281434e-141	-2.7652237220585614e-141

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	120	135
1	120	135

end0.0ms

sample817.0ms

Algorithm

intervals

Results

264.0ms	6556×	body	80	valid
78.0ms	516×	body	640	valid
48.0ms	1193×	body	80	invalid
47.0ms	263×	body	1280	valid
45.0ms	376×	body	320	valid
24.0ms	276×	body	160	valid
3.0ms	13×	body	2560	valid

Details

analyze1.1s

sample35.0ms

simplify63.0ms

prune4.0ms

localize9.0ms

rewrite34.0ms

series110.0ms

simplify45.0ms

prune174.0ms

localize25.0ms

rewrite59.0ms

series179.0ms

simplify43.0ms

prune175.0ms

localize21.0ms

rewrite71.0ms

series179.0ms

simplify51.0ms

prune171.0ms

localize17.0ms

rewrite125.0ms

series179.0ms

simplify74.0ms

prune213.0ms

regimes683.0ms

bsearch95.0ms

simplify3.0ms

end0.0ms

sample817.0ms

Profiling