Details

analyze998.0ms

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
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

sample29.0ms

Algorithm

intervals

Results

8.0ms	216×	body	128	valid
2.0ms	15×	body	512	valid
1.0ms	9×	body	1024	valid
1.0ms	15×	body	256	valid
1.0ms	13×	body	128	invalid
0.0ms	1×	body	2048	valid

simplify133.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4870	19
1	4870	19

prune2.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 16.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 z t) y)
2.6b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
11.2b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `associate-l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
4×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 69

Calls

3 calls:

7.0ms	(*.f64 (-.f64 z t) y)
12.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
10.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series578.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(*.f64 (-.f64 z t) y)
360.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
154.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

simplify36.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4986	1273
1	4986	1273

prune77.0ms

Filtered

57 candidates to 78 candidates (-36.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 4.3b

Counts

79 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a t))
0.5b	(cbrt.f64 (-.f64 a t))
3.6b	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
7.2b	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
30×	`associate-r_binary64`
27×	`cbrt-prod_binary64`
25×	`add-exp-log_binary64`
23×	`add-cube-cbrt_binary64`
18×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
17×	`associate-l_binary64`
10×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
9×	`add-log-exp_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64`
5×	`associate-r/_binary64` `associate-l/_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`diff-log_binary64` `pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 a t))
3.0ms	(cbrt.f64 (-.f64 a t))
33.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
10.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt.f64 (-.f64 a t))
207.0ms	(cbrt.f64 (-.f64 a t))
247.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
373.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5747	3545

prune123.0ms

Filtered

111 candidates to 138 candidates (-24.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	136	10	146

Merged error: 4.3b

Counts

146 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a t))
0.5b	(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))
2.3b	(.f64 (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))))
7.9b	(-.f64 (+.f64 x y) (.f64 (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t))))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

160×	`times-frac_binary64`
131×	`add-sqr-sqrt_binary64`
94×	`cbrt-div_binary64`
85×	`cbrt-prod_binary64`
80×	`associate-l_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
42×	`associate-/r/_binary64`
39×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
36×	`add-exp-log_binary64`
27×	`frac-times_binary64`
22×	`add-cbrt-cube_binary64`
20×	`unswap-sqr_binary64`
15×	`associate-r/_binary64` `associate-l/_binary64`
14×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
9×	`add-log-exp_binary64`
8×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`pow1_binary64` `div-inv_binary64` `frac-sub_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`diff-log_binary64` `pow1/3_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 218

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 a t))
10.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))
82.0ms	(.f64 (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))))
8.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt.f64 (-.f64 a t))
243.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))
281.0ms	(.f64 (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))))
381.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t))))))

simplify128.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5017	11551

prune265.0ms

Filtered

192 candidates to 230 candidates (-19.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	228	2	230
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	229	11	240

Merged error: 4.3b

Counts

240 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 z t))
0.6b	(cbrt.f64 (-.f64 z t))
1.5b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (cbrt.f64 (-.f64 a t))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))) (.f64 (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))))
8.6b	(-.f64 (+.f64 x y) (.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (cbrt.f64 (-.f64 a t))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))) (.f64 (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

510×	`cbrt-div_binary64`
312×	`add-exp-log_binary64`
151×	`frac-times_binary64`
137×	`add-cbrt-cube_binary64`
133×	`cbrt-undiv_binary64` `div-exp_binary64`
126×	`cbrt-unprod_binary64` `prod-exp_binary64`
112×	`flip3--_binary64` `flip--_binary64`
98×	`associate-l_binary64`
82×	`associate-/r/_binary64`
59×	`associate-*r/_binary64`
53×	`associate-*l/_binary64`
22×	`times-frac_binary64`
16×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
15×	`cbrt-prod_binary64`
14×	`frac-sub_binary64`
10×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64` `pow1_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
3×	`pow-prod-down_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`diff-log_binary64` `pow1/3_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `associate-r_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 271

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 z t))
4.0ms	(cbrt.f64 (-.f64 z t))
114.0ms	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (cbrt.f64 (-.f64 a t))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))) (.f64 (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))))
11.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (cbrt.f64 (-.f64 a t))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))) (.f64 (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

218.0ms	(cbrt.f64 (-.f64 z t))
215.0ms	(cbrt.f64 (-.f64 z t))
327.0ms	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (cbrt.f64 (-.f64 a t))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))) (.f64 (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))))
453.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (cbrt.f64 (-.f64 a t))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))) (.f64 (/.f64 y (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))))

simplify227.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5411	25540

prune457.0ms

Filtered

209 candidates to 283 candidates (-35.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	283	11	294

Merged error: 4.3b

Counts

294 → 11

regimes191.0ms

Accuracy

15.9% (5.5b remaining)

Error of 9.5b against oracle of 4.0b and baseline of 10.5b

bsearch51.0ms

Steps

Iters	Range		Point
9	9.354554485384638e-116	1.4083858596825023e-110	4.600289979140278e-113
6	-9.591287551873722e-23	-1.9307374506575663e-23	-1.9550660631378832e-23

simplify11.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	267	81
1	267	81

end0.0ms

sample728.0ms

Algorithm

intervals

Results

282.0ms	6818×	body	128	valid
49.0ms	460×	body	512	valid
47.0ms	326×	body	1024	valid
31.0ms	715×	body	128	invalid
24.0ms	328×	body	256	valid
13.0ms	68×	body	2048	valid

Details

analyze998.0ms

sample29.0ms

simplify133.0ms

prune2.0ms

localize9.0ms

rewrite34.0ms

series578.0ms

simplify36.0ms

prune77.0ms

localize14.0ms

rewrite67.0ms

series1.0s

simplify67.0ms

prune123.0ms

localize18.0ms

rewrite151.0ms

series1.1s

simplify128.0ms

prune265.0ms

localize35.0ms

rewrite239.0ms

series1.2s

simplify227.0ms

prune457.0ms

regimes191.0ms

bsearch51.0ms

simplify11.0ms

end0.0ms

sample728.0ms

Profiling