Details

analyze692.0ms

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample38.0ms

Algorithm

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	14×	body	128	nan
1.0ms	10×	body	128	invalid

simplify487.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (317.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune8.0ms

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: 19.5b

Counts

2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
124.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
136.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5216	2053

prune164.0ms

Filtered

69 candidates to 87 candidates (-26.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Merged error: 6.4b

Counts

88 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
2.7b	(/.f64 c (.f64 2 (-.f64 b (/.f64 (.f64 c a) b))))
5.3b	(/.f64 (*.f64 c a) b)
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-/l*_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`flip3--_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64`

Counts

4 → 89

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
9.0ms	(/.f64 c (.f64 2 (-.f64 b (/.f64 (.f64 c a) b))))
5.0ms	(/.f64 (*.f64 c a) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
248.0ms	(/.f64 c (.f64 2 (-.f64 b (/.f64 (.f64 c a) b))))
35.0ms	(/.f64 (*.f64 c a) b)
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify42.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5114	1923

prune140.0ms

Filtered

74 candidates to 101 candidates (-36.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	96	12	108

Merged error: 4.7b

Counts

108 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
2.7b	(/.f64 c (*.f64 2 (-.f64 b (/.f64 c (/.f64 b a)))))
3.9b	(/.f64 c (/.f64 b a))
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`associate-/r*_binary64`
12×	`associate-/l*_binary64`
7×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
5×	`pow1_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`flip3--_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64`

Counts

4 → 138

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
19.0ms	(/.f64 c (*.f64 2 (-.f64 b (/.f64 c (/.f64 b a)))))
6.0ms	(/.f64 c (/.f64 b a))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
239.0ms	(/.f64 c (*.f64 2 (-.f64 b (/.f64 c (/.f64 b a)))))
37.0ms	(/.f64 c (/.f64 b a))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify69.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5321	2906

prune224.0ms

Filtered

117 candidates to 150 candidates (-28.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	147	15	162

Merged error: 4.7b

Counts

162 → 15

localize32.0ms

Local error

Found 4 expressions with local error:

1.5b	(/.f64 b (*.f64 a (cbrt.f64 c)))
2.7b	(/.f64 c (.f64 2 (-.f64 b (/.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (/.f64 b (*.f64 a (cbrt.f64 c)))))))
2.9b	(/.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (/.f64 b (.f64 a (cbrt.f64 c))))
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log_binary64`
26×	`add-cbrt-cube_binary64`
19×	`times-frac_binary64`
14×	`cbrt-undiv_binary64` `add-sqr-sqrt_binary64` `div-exp_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-/r*_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `associate-*r/_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 97

Calls

4 calls:

5.0ms	(/.f64 b (*.f64 a (cbrt.f64 c)))
12.0ms	(/.f64 c (.f64 2 (-.f64 b (/.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (/.f64 b (*.f64 a (cbrt.f64 c)))))))
11.0ms	(/.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (/.f64 b (.f64 a (cbrt.f64 c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.f64 b (*.f64 a (cbrt.f64 c)))
388.0ms	(/.f64 c (.f64 2 (-.f64 b (/.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (/.f64 b (*.f64 a (cbrt.f64 c)))))))
94.0ms	(/.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (/.f64 b (.f64 a (cbrt.f64 c))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify58.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4996	1640
1	4996	1640

prune119.0ms

Filtered

78 candidates to 109 candidates (-39.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	109	15	124

Merged error: 4.7b

Counts

124 → 15

regimes204.0ms

Accuracy

88.9% (1.7b remaining)

Error of 7.1b against oracle of 5.4b and baseline of 21.0b

bsearch75.0ms

Steps

Iters	Range		Point
10	1.5169449378701754e-09	23.54655251284956	23.282155229196768
5	-2.257216897950517e+143	-7.310512280228855e+142	-1.6744801799035577e+143

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	118	151
1	118	151

end0.0ms

sample933.0ms

Algorithm

intervals

Results

655.0ms	8000×	body	128	valid
48.0ms	646×	body	128	nan
30.0ms	384×	body	128	invalid

Details

analyze692.0ms

sample38.0ms

simplify487.0ms

prune8.0ms

localize30.0ms

rewrite30.0ms

series720.0ms

simplify51.0ms

prune164.0ms

localize24.0ms

rewrite34.0ms

series577.0ms

simplify42.0ms

prune140.0ms

localize24.0ms

rewrite52.0ms

series568.0ms

simplify69.0ms

prune224.0ms

localize32.0ms

rewrite37.0ms

series697.0ms

simplify58.0ms

prune119.0ms

regimes204.0ms

bsearch75.0ms

simplify4.0ms

end0.0ms

sample933.0ms

Profiling