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%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

sample33.0ms

Algorithm

intervals

Results

8.0ms	207×	body	80	valid
3.0ms	23×	body	640	valid
2.0ms	40×	body	80	invalid
1.0ms	6×	body	1280	valid
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	2560	valid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4885	13
1	4885	13

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: 13.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
4.0b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
4.6b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
23×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 119

Calls

3 calls:

8.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
4.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
18.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
71.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
56.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

simplify45.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5183	1602

prune110.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	114	14	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	14	129

Merged error: 4.3b

Counts

129 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
1.9b	(.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))))
8.1b	(+.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)))))

rewrite60.0ms

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))
4.0ms	(cbrt.f64 (-.f64 a z))
41.0ms	(.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)))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(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))))
56.0ms	(+.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 (26.0ms)

Iter	Nodes	Cost
0	5292	2530

prune116.0ms

Filtered

110 candidates to 146 candidates (-32.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	145	15	160

Merged error: 4.0b

Counts

160 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 (-.f64 a z)))
0.6b	(cbrt.f64 (cbrt.f64 (-.f64 a z)))
1.8b	(.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)))))
8.3b	(+.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))))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64`
100×	`cbrt-prod_binary64`
98×	`times-frac_binary64`
76×	`*-un-lft-identity_binary64`
69×	`add-exp-log_binary64`
61×	`associate-r_binary64`
48×	`cbrt-div_binary64`
42×	`add-cbrt-cube_binary64`
38×	`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 → 189

Calls

4 calls:

4.0ms	(cbrt.f64 (cbrt.f64 (-.f64 a z)))
4.0ms	(cbrt.f64 (cbrt.f64 (-.f64 a z)))
70.0ms	(.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)))))
6.0ms	(+.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))))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (cbrt.f64 (-.f64 a z)))
26.0ms	(cbrt.f64 (cbrt.f64 (-.f64 a z)))
66.0ms	(.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)))))
57.0ms	(+.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))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4983	5043
1	4983	5043

prune142.0ms

Filtered

147 candidates to 201 candidates (-36.7%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	200	16	216

Merged error: 4.0b

Counts

216 → 16

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
1.1b	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
1.1b	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
9.8b	(+.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))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

213×	`cbrt-prod_binary64`
139×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64`
39×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`cbrt-div_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3--_binary64` `pow1/3_binary64` `div-inv_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 176

Calls

4 calls:

10.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
9.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
9.0ms	(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))))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
69.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
70.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
59.0ms	(+.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))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5205	3747

prune85.0ms

Filtered

143 candidates to 188 candidates (-31.5%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	13	13
Picked	0	1	1
Done	0	2	2
Total	188	16	204

Merged error: 4.0b

Counts

204 → 16

regimes586.0ms

Accuracy

46.6% (4.7b remaining)

Error of 8.5b against oracle of 3.7b and baseline of 12.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	95
1	80	95

end0.0ms

sample812.0ms

Algorithm

intervals

Results

257.0ms	6533×	body	80	valid
77.0ms	496×	body	640	valid
51.0ms	268×	body	1280	valid
49.0ms	1205×	body	80	invalid
48.0ms	401×	body	320	valid
20.0ms	279×	body	160	valid
5.0ms	23×	body	2560	valid

Details

analyze1.1s

sample33.0ms

simplify79.0ms

prune3.0ms

localize9.0ms

rewrite37.0ms

series142.0ms

simplify45.0ms

prune110.0ms

localize13.0ms

rewrite60.0ms

series177.0ms

simplify43.0ms

prune116.0ms

localize17.0ms

rewrite102.0ms

series174.0ms

simplify72.0ms

prune142.0ms

localize18.0ms

rewrite49.0ms

series267.0ms

simplify62.0ms

prune85.0ms

regimes586.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample812.0ms

Profiling