Details

analyze420.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample37.0ms

Algorithm

intervals

Results

8.0ms	172×	body	80	valid
7.0ms	28×	body	2560	valid
5.0ms	27×	body	1280	valid
2.0ms	12×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	21×	body	80	nan
0.0ms	3×	body	160	valid
0.0ms	1×	body	80	invalid

simplify627.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	715	18
1	715	18

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 34.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
10.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
94.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
84.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5703	2155

prune92.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Merged error: 8.5b

Counts

95 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.1b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
12.7b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
32×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `div-inv_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 217

Calls

4 calls:

7.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
14.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
144.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
184.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify129.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5766	8137

prune163.0ms

Filtered

175 candidates to 229 candidates (-30.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	229	8	237

Merged error: 8.3b

Counts

237 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
1.0b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
177.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
55.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4935	1690
1	4935	1690

prune53.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	83	8	91

Merged error: 8.3b

Counts

91 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b	(.f64 (/.f64 a (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (/.f64 (neg.f64 c) (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
3.1b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (/.f64 (neg.f64 c) (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))) a)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac_binary64`
96×	`add-sqr-sqrt_binary64`
90×	`*-un-lft-identity_binary64`
76×	`associate-r_binary64`
64×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`associate-l_binary64`
21×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
13×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-div_binary64`
7×	`neg-mul-1_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`associate-/l/_binary64` `associate-/r*_binary64` `div-inv_binary64` `distribute-frac-neg_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `distribute-rgt-neg-out_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`

Counts

4 → 194

Calls

4 calls:

55.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (/.f64 (neg.f64 c) (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
24.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (/.f64 (neg.f64 c) (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (/.f64 (neg.f64 c) (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
157.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (/.f64 (neg.f64 c) (sqrt.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))) a)
57.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
54.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5464	7204

prune128.0ms

Filtered

129 candidates to 206 candidates (-59.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	206	8	214

Merged error: 8.3b

Counts

214 → 8

regimes97.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.6b

bsearch84.0ms

Steps

Iters	Range	Point
6	2.080907647498648e+117	1.3327544757021516e+118	4.1131887417592497e+117
9	-2.2927681493181693e-300	-1.9071692092543137e-308	-2.1924358107857753e-301
8	-1.6720270200784007e+116	-8.039793483863018e+112	-2.817222120419214e+114

Iters

Range

Point

2.080907647498648e+117

1.3327544757021516e+118

4.1131887417592497e+117

-2.2927681493181693e-300

-1.9071692092543137e-308

-2.1924358107857753e-301

-1.6720270200784007e+116

-8.039793483863018e+112

-2.817222120419214e+114

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	85
1	101	85

end0.0ms

sample1.1s

Algorithm

intervals

Results

260.0ms	1046×	body	2560	valid
228.0ms	5167×	body	80	valid
188.0ms	917×	body	1280	valid
74.0ms	441×	body	640	valid
34.0ms	108×	body	5120	valid
33.0ms	797×	body	80	nan
26.0ms	220×	body	320	valid
11.0ms	249×	body	80	invalid
8.0ms	101×	body	160	valid

Details

analyze420.0ms

sample37.0ms

simplify627.0ms

prune7.0ms

localize10.0ms

rewrite32.0ms

series267.0ms

simplify91.0ms

prune92.0ms

localize10.0ms

rewrite44.0ms

series447.0ms

simplify129.0ms

prune163.0ms

localize10.0ms

rewrite24.0ms

series318.0ms

simplify84.0ms

prune53.0ms

localize17.0ms

rewrite99.0ms

series478.0ms

simplify123.0ms

prune128.0ms

regimes97.0ms

bsearch84.0ms

simplify5.0ms

end0.0ms

sample1.1s

Profiling