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

sample40.0ms

Algorithm

intervals

Results

9.0ms	202×	body	80	valid
3.0ms	22×	body	320	valid
2.0ms	16×	body	640	valid
2.0ms	41×	body	80	invalid
1.0ms	5×	body	1280	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4934	19
1	4934	19

prune8.0ms

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: 17.1b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
3.3b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
6.6b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64_3127`
73×	`*-un-lft-identity_binary64_3142`
51×	`times-frac_binary64_3137`
31×	`associate-r_binary64_3201`
27×	`add-cube-cbrt_binary64_3113`
23×	`distribute-lft-out--_binary64_3187` `difference-of-squares_binary64_3171`
10×	`add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106`
5×	`associate-/l_binary64_3206` `associate-l_binary64_3202` `associate-/r_binary64_3205` `pow1_binary64_3088` `flip--_binary64_3168` `flip3--_binary64_3141` `add-log-exp_binary64_3107`
4×	`associate-/r/_binary64_3207`
2×	`associate-/l/_binary64_3208` `cbrt-undiv_binary64_3112` `div-exp_binary64_3095` `frac-times_binary64_3134` `cbrt-unprod_binary64_3111` `unswap-sqr_binary64_3170` `associate-*l/_binary64_3204` `div-inv_binary64_3143` `prod-exp_binary64_3093`
1×	`div-sub_binary64_3136` `clear-num_binary64_3145` `pow-prod-down_binary64_3069` `+-commutative_binary64_3209` `flip-+_binary64_3167` `frac-2neg_binary64_3135` `sum-log_binary64_3057` `associate-r/_binary64_3203` `-commutative_binary64_3210` `flip3-+_binary64_3140`

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)))

series451.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
220.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
164.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

simplify80.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5178	2420

prune498.0ms

Filtered

90 candidates to 128 candidates (-42.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	114	14	128
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	15	129

Merged error: 2.7b

Counts

129 → 15

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
1.0b	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
9.6b	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log_binary64_3106`
17×	`add-sqr-sqrt_binary64_3127`
16×	`cbrt-div_binary64_3110`
14×	`add-cbrt-cube_binary64_3114` `*-un-lft-identity_binary64_3142`
13×	`associate-r_binary64_3201`
10×	`cbrt-prod_binary64_3109` `flip--_binary64_3168` `flip3--_binary64_3141`
9×	`cbrt-unprod_binary64_3111` `prod-exp_binary64_3093`
8×	`associate-/r/_binary64_3207` `add-cube-cbrt_binary64_3113`
6×	`frac-times_binary64_3134` `pow1_binary64_3088` `add-log-exp_binary64_3107`
5×	`associate-l_binary64_3202`
4×	`cbrt-undiv_binary64_3112` `div-exp_binary64_3095` `associate-*l/_binary64_3204`
3×	`distribute-lft-out--_binary64_3187` `difference-of-squares_binary64_3171` `associate-*r/_binary64_3203`
2×	`unswap-sqr_binary64_3170` `pow1/3_binary64_3080` `times-frac_binary64_3137`
1×	`pow-prod-down_binary64_3069` `+-commutative_binary64_3209` `flip-+_binary64_3167` `sum-log_binary64_3057` `*-commutative_binary64_3210` `flip3-+_binary64_3140` `div-inv_binary64_3143`

Counts

4 → 85

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
27.0ms	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
5.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt.f64 (-.f64 a z))
112.0ms	(cbrt.f64 (-.f64 a z))
569.0ms	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
238.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5739	2739

prune420.0ms

Filtered

79 candidates to 97 candidates (-22.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	97	15	112

Merged error: 2.7b

Counts

112 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

8.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
8.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
8.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
10.1b	(+.f64 x (.f64 (.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity_binary64_3142` `add-sqr-sqrt_binary64_3127`
93×	`cbrt-prod_binary64_3109`
75×	`times-frac_binary64_3137`
37×	`add-cube-cbrt_binary64_3113`
30×	`distribute-lft-out--_binary64_3187` `difference-of-squares_binary64_3171`
6×	`associate-/r/_binary64_3207` `add-log-exp_binary64_3107`
4×	`pow1_binary64_3088` `add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106`
3×	`cbrt-div_binary64_3110` `pow1/3_binary64_3080` `flip--_binary64_3168` `flip3--_binary64_3141` `div-inv_binary64_3143`
1×	`+-commutative_binary64_3209` `flip-+_binary64_3167` `sum-log_binary64_3057` `flip3-+_binary64_3140`

Counts

4 → 131

Calls

4 calls:

8.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
7.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
7.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
5.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))))

series925.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
230.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
231.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
234.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5180	3666

prune532.0ms

Filtered

107 candidates to 143 candidates (-33.6%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	143	15	158

Merged error: 2.7b

Counts

158 → 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))
6.6b	(.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))))
8.4b	(+.f64 x (.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac_binary64_3137`
142×	`associate-r_binary64_3201`
128×	`add-sqr-sqrt_binary64_3127`
114×	`*-un-lft-identity_binary64_3142`
102×	`cbrt-div_binary64_3110`
97×	`cbrt-prod_binary64_3109`
66×	`associate-/r/_binary64_3207`
58×	`add-cube-cbrt_binary64_3113`
53×	`flip--_binary64_3168` `flip3--_binary64_3141`
34×	`frac-times_binary64_3134`
28×	`distribute-lft-out--_binary64_3187` `difference-of-squares_binary64_3171`
18×	`associate-*l/_binary64_3204` `add-exp-log_binary64_3106`
17×	`associate-*r/_binary64_3203`
13×	`add-cbrt-cube_binary64_3114`
9×	`div-inv_binary64_3143`
6×	`pow1_binary64_3088` `add-log-exp_binary64_3107`
5×	`associate-l_binary64_3202` `cbrt-undiv_binary64_3112` `div-exp_binary64_3095` `cbrt-unprod_binary64_3111` `unswap-sqr_binary64_3170` `prod-exp_binary64_3093`
2×	`pow1/3_binary64_3080`
1×	`pow-prod-down_binary64_3069` `+-commutative_binary64_3209` `flip-+_binary64_3167` `sum-log_binary64_3057` `*-commutative_binary64_3210` `flip3-+_binary64_3140`

Counts

4 → 215

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
54.0ms	(.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))))
12.0ms	(+.f64 x (.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))))

series649.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt.f64 (-.f64 a z))
120.0ms	(cbrt.f64 (-.f64 a z))
172.0ms	(.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))))
235.0ms	(+.f64 x (.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))))

simplify111.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5534	7322

prune889.0ms

Filtered

174 candidates to 227 candidates (-30.5%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	11	11
Picked	0	1	1
Done	1	2	3
Total	227	15	242

Merged error: 2.7b

Counts

242 → 15

regimes1.3s

Accuracy

66.9% (3.8b remaining)

Error of 7.1b against oracle of 3.3b and baseline of 14.7b

bsearch2.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	234
1	82	234

end0.0ms

sample960.0ms

Algorithm

intervals

Results

296.0ms	6561×	body	80	valid
77.0ms	475×	body	640	valid
53.0ms	1196×	body	80	invalid
50.0ms	446×	body	320	valid
44.0ms	240×	body	1280	valid
20.0ms	258×	body	160	valid
5.0ms	20×	body	2560	valid

Details

analyze1.1s

sample40.0ms

simplify120.0ms

prune8.0ms

localize14.0ms

rewrite36.0ms

series451.0ms

simplify80.0ms

prune498.0ms

localize29.0ms

rewrite42.0ms

series1.0s

simplify63.0ms

prune420.0ms

localize26.0ms

rewrite35.0ms

series925.0ms

simplify83.0ms

prune532.0ms

localize21.0ms

rewrite95.0ms

series649.0ms

simplify111.0ms

prune889.0ms

regimes1.3s

bsearch2.0ms

simplify5.0ms

end0.0ms

sample960.0ms

Profiling