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
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample33.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	73×	body	80	nan
2.0ms	34×	body	80	invalid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune4.0ms

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: 24.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
5.3b	(.f64 (.f64 x y) z)
7.8b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
22.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/r/_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
5.0ms	(.f64 (.f64 x y) z)
10.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 z z) (.f64 t a))
7.0ms	(.f64 (.f64 x y) z)
35.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
20.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify36.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5307	972

prune106.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Merged error: 3.0b

Counts

88 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.6b	(-.f64 (.f64 z z) (.f64 t a))
3.0b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
22.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`associate-r_binary64` `sqrt-prod_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`div-inv_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))
12.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
195.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
8.0ms	(-.f64 (.f64 z z) (.f64 t a))
36.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
15.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5256	1640

prune105.0ms

Filtered

83 candidates to 123 candidates (-48.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	121	10	131

Merged error: 3.0b

Counts

131 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
0.7b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
2.1b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
22.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`sqrt-prod_binary64`
12×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`pow-prod-down_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `flip--_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
11.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
11.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 z z) (.f64 t a))
22.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
38.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
15.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune93.0ms

Filtered

68 candidates to 103 candidates (-51.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	102	11	113

Merged error: 3.0b

Counts

113 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

14.0b	(cbrt.f64 (.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
22.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
2×	`associate-*r/_binary64`
1×	`cbrt-div_binary64` `pow1/3_binary64` `cbrt-prod_binary64`

Counts

4 → 55

Calls

4 calls:

9.0ms	(cbrt.f64 (.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt.f64 (.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
15.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
15.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
17.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify43.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5328	788

prune60.0ms

Filtered

57 candidates to 67 candidates (-17.5%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	67	11	78

Merged error: 3.0b

Counts

78 → 11

regimes940.0ms

Accuracy

84.1% (3.0b remaining)

Error of 6.5b against oracle of 3.4b and baseline of 22.5b

bsearch120.0ms

Steps

Iters	Range		Point
8	2.3182363157074874e+140	2.4327913402753088e+143	1.0018756625348413e+142
9	-3.0273427999488094e-280	-1.2904722683531297e-288	-2.403671892753973e-282
10	-8.421225428739286e-151	-2.432862960168308e-165	-4.636365954139031e-158
8	-5.636726367833887e+92	-7.924427136884148e+89	-5.539714192103757e+92

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	65
1	80	65

end0.0ms

sample1.1s

Algorithm

intervals

Results

494.0ms	8000×	body	80	valid
127.0ms	2234×	body	80	nan
54.0ms	898×	body	80	invalid

Details

analyze1.1s

sample33.0ms

simplify39.0ms

prune4.0ms

localize10.0ms

rewrite25.0ms

series71.0ms

simplify36.0ms

prune106.0ms

localize10.0ms

rewrite222.0ms

series74.0ms

simplify53.0ms

prune105.0ms

localize10.0ms

rewrite33.0ms

series83.0ms

simplify48.0ms

prune93.0ms

localize17.0ms

rewrite23.0ms

series123.0ms

simplify43.0ms

prune60.0ms

regimes940.0ms

bsearch120.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling