Details

analyze818.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample46.0ms

Algorithm

intervals

Results

11.0ms	192×	body	80	valid
7.0ms	22×	body	2560	valid
7.0ms	26×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	37	26
1	37	26

prune13.0ms

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: 14.2b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.6b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
13.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_1858`
21×	`add-sqr-sqrt_binary64_1843`
20×	`add-cube-cbrt_binary64_1829`
18×	`times-frac_binary64_1853`
16×	`sqrt-prod_binary64_1837`
8×	`pow1_binary64_1804`
6×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822` `associate-/r*_binary64_1921` `sqrt-div_binary64_1838` `add-log-exp_binary64_1823`
4×	`flip3-+_binary64_1856` `flip-+_binary64_1883`
3×	`sqrt-pow1_binary64_1839` `associate-/l*_binary64_1922`
2×	`associate-/r/_binary64_1923` `associate-*r/_binary64_1919` `pow1/2_binary64_1794`
1×	`+-commutative_binary64_1925` `div-exp_binary64_1811` `cbrt-undiv_binary64_1828` `sum-log_binary64_1773` `clear-num_binary64_1861` `frac-2neg_binary64_1851` `distribute-lft-out_binary64_1902` `div-inv_binary64_1859` `pow-prod-down_binary64_1785` `rem-sqrt-square_binary64_1846`

Counts

4 → 81

Calls

4 calls:

15.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
34.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
46.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
35.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5307	2240

prune455.0ms

Filtered

74 candidates to 93 candidates (-25.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	80	13	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	13	94

Merged error: 13.9b

Counts

94 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
2.5b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64_1843`
40×	`times-frac_binary64_1853`
36×	`*-un-lft-identity_binary64_1858`
34×	`add-cube-cbrt_binary64_1829`
26×	`sqrt-prod_binary64_1837`
24×	`associate-r_binary64_1917`
14×	`add-exp-log_binary64_1822`
11×	`add-cbrt-cube_binary64_1830`
9×	`pow1_binary64_1804`
6×	`associate-/r*_binary64_1921` `sqrt-div_binary64_1838` `add-log-exp_binary64_1823`
5×	`unswap-sqr_binary64_1886`
4×	`associate-/r/_binary64_1923` `flip3-+_binary64_1856` `flip-+_binary64_1883`
3×	`pow-flip_binary64_1788` `associate-l_binary64_1918` `prod-exp_binary64_1809` `associate-/l*_binary64_1922`
2×	`div-exp_binary64_1811` `cbrt-undiv_binary64_1828` `cbrt-unprod_binary64_1827` `rec-exp_binary64_1810` `sqrt-pow1_binary64_1839` `div-inv_binary64_1859` `pow1/2_binary64_1794`
1×	`+-commutative_binary64_1925` `sum-log_binary64_1773` `clear-num_binary64_1861` `frac-2neg_binary64_1851` `-commutative_binary64_1926` `inv-pow_binary64_1780` `associate-r/_binary64_1919` `pow-prod-down_binary64_1785` `rem-sqrt-square_binary64_1846` `un-div-inv_binary64_1860`

Counts

4 → 120

Calls

4 calls:

9.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
15.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
3.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
34.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
48.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
33.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify131.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4933	2849
1	4933	2849

prune514.0ms

Filtered

87 candidates to 132 candidates (-51.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	134	11	145

Merged error: 13.9b

Counts

145 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
8.8b	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod_binary64_1837`
50×	`add-sqr-sqrt_binary64_1843`
34×	`sqrt-pow1_binary64_1839`
29×	`pow1_binary64_1804`
28×	`sqrt-div_binary64_1838`
20×	`*-un-lft-identity_binary64_1858`
18×	`add-cube-cbrt_binary64_1829` `pow1/2_binary64_1794`
15×	`swap-sqr_binary64_1885`
9×	`associate-l_binary64_1918` `associate-r_binary64_1917` `unswap-sqr_binary64_1886` `pow-prod-up_binary64_1784` `flip3-+_binary64_1856` `flip-+_binary64_1883`
6×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822` `add-log-exp_binary64_1823`
5×	`pow-sqr_binary64_1891` `pow-prod-down_binary64_1785`
4×	`frac-times_binary64_1850`
2×	`associate-l/_binary64_1920` `associate-r/_binary64_1919` `rem-sqrt-square_binary64_1846`
1×	`pow2_binary64_1795` `+-commutative_binary64_1925` `sum-log_binary64_1773` `cbrt-unprod_binary64_1827` `prod-exp_binary64_1809` `distribute-lft-out_binary64_1902` `*-commutative_binary64_1926` `sqrt-unprod_binary64_1841` `pow-plus_binary64_1799` `rem-square-sqrt_binary64_1845`

Counts

4 → 125

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
12.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
12.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
49.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
27.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
29.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify138.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4975	2838
1	4975	2838

prune478.0ms

Filtered

84 candidates to 137 candidates (-63.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	137	11	148

Merged error: 13.9b

Counts

148 → 11

localize49.0ms

Local error

Found 4 expressions with local error:

6.6b	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
13.3b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
14.3b	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.3b	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_1858`
8×	`add-sqr-sqrt_binary64_1843`
7×	`add-cube-cbrt_binary64_1829`
6×	`cbrt-prod_binary64_1825` `add-log-exp_binary64_1823`
5×	`pow1_binary64_1804`
4×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822` `cbrt-div_binary64_1826` `flip3-+_binary64_1856` `flip-+_binary64_1883`
3×	`sqrt-prod_binary64_1837`
2×	`pow1/3_binary64_1796` `sqrt-div_binary64_1838`
1×	`+-commutative_binary64_1925` `sum-log_binary64_1773` `distribute-lft-out_binary64_1902` `sqrt-pow1_binary64_1839` `pow1/2_binary64_1794` `rem-sqrt-square_binary64_1846`

Counts

4 → 53

Calls

4 calls:

12.0ms	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
7.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(+.f64 1 (/.f64 x (.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
29.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
98.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
99.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

simplify94.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5077	2219

prune331.0ms

Filtered

59 candidates to 65 candidates (-10.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	66	10	76

Merged error: 13.9b

Counts

76 → 10

regimes229.0ms

Accuracy

0% (1.3b remaining)

Error of 14.3b against oracle of 13.0b and baseline of 14.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	47
1	22	47

end0.0ms

sample1.2s

Algorithm

intervals

Results

338.0ms	6026×	body	80	valid
264.0ms	817×	body	2560	valid
157.0ms	614×	body	1280	valid
135.0ms	8000×	pre	80	true
62.0ms	296×	body	640	valid
28.0ms	157×	body	320	valid
9.0ms	90×	body	160	valid

Details

analyze818.0ms

sample46.0ms

simplify18.0ms

prune13.0ms

localize18.0ms

rewrite46.0ms

series219.0ms

simplify79.0ms

prune455.0ms

localize20.0ms

rewrite39.0ms

series151.0ms

simplify131.0ms

prune514.0ms

localize22.0ms

rewrite57.0ms

series138.0ms

simplify138.0ms

prune478.0ms

localize49.0ms

rewrite31.0ms

series528.0ms

simplify94.0ms

prune331.0ms

regimes229.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling