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

sample37.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	71×	body	80	nan
1.0ms	28×	body	80	invalid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

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: 25.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
4.9b	(.f64 (.f64 x y) z)
9.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
24.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite26.0ms

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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 z z) (.f64 t a))
7.0ms	(.f64 (.f64 x y) z)
37.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
15.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify37.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5307	972

prune86.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	10	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	10	88

Merged error: 3.8b

Counts

88 → 10

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))
3.3b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
24.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite32.0ms

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))))
5.0ms	(-.f64 (.f64 z z) (.f64 t a))
13.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
8.0ms	(-.f64 (.f64 z z) (.f64 t a))
46.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
20.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5256	1640

prune63.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	124	9	133

Merged error: 3.6b

Counts

133 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
0.6b	(-.f64 (.f64 z z) (.f64 t a))
3.4b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
24.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac_binary64`
47×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
33×	`sqrt-prod_binary64`
25×	`associate-/r*_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`div-inv_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 131

Calls

4 calls:

7.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
4.0ms	(-.f64 (.f64 z z) (.f64 t a))
13.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
8.0ms	(-.f64 (.f64 z z) (.f64 t a))
34.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
14.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5053	2219

prune75.0ms

Filtered

98 candidates to 143 candidates (-45.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	143	9	152

Merged error: 3.5b

Counts

152 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
1.4b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
2.2b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
24.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite38.0ms

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:

6.0ms	(-.f64 (.f64 z z) (.f64 t a))
12.0ms	(.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)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 z z) (.f64 t a))
21.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
34.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
14.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune35.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 3.5b

Counts

112 → 9

regimes576.0ms

Accuracy

84.2% (3.0b remaining)

Error of 6.4b against oracle of 3.4b and baseline of 22.6b

bsearch58.0ms

Steps

Iters	Range		Point
10	9.185335006362514e+59	4.9999381530526934e+73	4.433126571344847e+73
9	-1.2526406023323622e+125	-1.6016063649402293e+120	-1.1318662440682364e+125

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	29
1	68	29

end0.0ms

sample922.0ms

Algorithm

intervals

Results

417.0ms	8000×	body	80	valid
109.0ms	2291×	body	80	nan
52.0ms	867×	body	80	invalid

Details

analyze1.1s

sample37.0ms

simplify38.0ms

prune3.0ms

localize10.0ms

rewrite26.0ms

series67.0ms

simplify37.0ms

prune86.0ms

localize10.0ms

rewrite32.0ms

series86.0ms

simplify55.0ms

prune63.0ms

localize10.0ms

rewrite34.0ms

series72.0ms

simplify49.0ms

prune75.0ms

localize10.0ms

rewrite38.0ms

series77.0ms

simplify52.0ms

prune35.0ms

regimes576.0ms

bsearch58.0ms

simplify2.0ms

end0.0ms

sample922.0ms

Profiling