Details

analyze1.0s

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

sample30.0ms

Algorithm

intervals

Results

8.0ms	214×	body	80	valid
2.0ms	59×	body	80	invalid
2.0ms	13×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	11×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4892	13
1	4892	13

prune9.0ms

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: 24.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y z) (-.f64 t x))
3.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
17.6b	(/.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))

series121.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
63.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
47.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	6037	1081

prune123.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 2.9b

Counts

89 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
1.5b	(.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))))
7.4b	(+.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)))))

rewrite57.0ms

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:

3.0ms	(cbrt.f64 (-.f64 a z))
5.0ms	(cbrt.f64 (-.f64 a z))
37.0ms	(.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))))
5.0ms	(+.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)))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt.f64 (-.f64 a z))
30.0ms	(cbrt.f64 (-.f64 a z))
81.0ms	(.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))))
62.0ms	(+.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)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5292	2530

prune143.0ms

Filtered

110 candidates to 146 candidates (-32.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	145	9	154

Merged error: 2.5b

Counts

154 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
2.0b	(.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
6.9b	(+.f64 x (.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt_binary64`
98×	`times-frac_binary64`
84×	`cbrt-prod_binary64`
74×	`*-un-lft-identity_binary64`
69×	`add-exp-log_binary64`
61×	`associate-r_binary64`
44×	`cbrt-div_binary64`
42×	`add-cbrt-cube_binary64`
36×	`add-cube-cbrt_binary64`
29×	`associate-l_binary64`
27×	`cbrt-undiv_binary64` `div-exp_binary64`
24×	`cbrt-unprod_binary64` `prod-exp_binary64`
19×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
18×	`associate-/r/_binary64`
15×	`flip3--_binary64` `flip--_binary64`
12×	`unswap-sqr_binary64`
9×	`frac-times_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`associate-r/_binary64` `associate-l/_binary64`
3×	`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 → 183

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
68.0ms	(.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (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)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt.f64 (-.f64 a z))
28.0ms	(cbrt.f64 (-.f64 a z))
76.0ms	(.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
69.0ms	(+.f64 x (.f64 (/.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4984	4919
1	4984	4919

prune187.0ms

Filtered

141 candidates to 195 candidates (-38.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	195	9	204

Merged error: 2.5b

Counts

204 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
0.6b	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
1.2b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))
7.9b	(+.f64 x (.f64 (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

142×	`cbrt-prod_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64`
86×	`times-frac_binary64`
44×	`add-cube-cbrt_binary64`
27×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
26×	`cbrt-div_binary64`
25×	`add-exp-log_binary64`
17×	`associate-l_binary64`
15×	`add-cbrt-cube_binary64`
12×	`associate-/r/_binary64`
11×	`cbrt-unprod_binary64` `prod-exp_binary64`
9×	`pow1_binary64` `frac-times_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`associate-*r/_binary64`
6×	`add-log-exp_binary64`
5×	`associate-*l/_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `div-inv_binary64`
2×	`pow1/3_binary64` `unswap-sqr_binary64`
1×	`flip3-+_binary64` `associate-r_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 170

Calls

4 calls:

9.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
9.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
42.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (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)))) (.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
73.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
156.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))
66.0ms	(+.f64 x (.f64 (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5513	4166

prune143.0ms

Filtered

132 candidates to 182 candidates (-37.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	181	10	191

Merged error: 2.5b

Counts

191 → 10

regimes458.0ms

Accuracy

14.6% (7.9b remaining)

Error of 11.2b against oracle of 3.2b and baseline of 12.5b

bsearch38.0ms

Steps

Iters	Range		Point
9	4.62183871278111e-173	3.648303785268756e-167	1.5504634327615182e-167
4	-7.998888117147235e-69	-5.137629488081729e-69	-5.227043820240027e-69

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	69
1	71	69

end0.0ms

sample826.0ms

Algorithm

intervals

Results

268.0ms	6566×	body	80	valid
79.0ms	492×	body	640	valid
50.0ms	403×	body	320	valid
49.0ms	269×	body	1280	valid
48.0ms	1167×	body	80	invalid
19.0ms	255×	body	160	valid
3.0ms	15×	body	2560	valid

Details

analyze1.0s

sample30.0ms

simplify64.0ms

prune9.0ms

localize9.0ms

rewrite34.0ms

series121.0ms

simplify53.0ms

prune123.0ms

localize13.0ms

rewrite57.0ms

series201.0ms

simplify42.0ms

prune143.0ms

localize18.0ms

rewrite92.0ms

series203.0ms

simplify74.0ms

prune187.0ms

localize17.0ms

rewrite73.0ms

series367.0ms

simplify53.0ms

prune143.0ms

regimes458.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample826.0ms

Profiling