Details

analyze491.0ms

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample35.0ms

Algorithm

intervals

Results

22.0ms	256×	body	128	valid
2.0ms	30×	body	128	nan
1.0ms	8×	body	128	invalid

simplify324.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (316.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune5.0ms

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: 16.6b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4983	1445
1	4983	1445

prune117.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 5.0b

Counts

69 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.2b	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
4.4b	(/.f64 (*.f64 a c) b)
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r*_binary64` `times-frac_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3--_binary64` `associate-r/_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
14.0ms	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
128.0ms	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
32.0ms	(/.f64 (*.f64 a c) b)
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5056	1264

prune107.0ms

Filtered

58 candidates to 83 candidates (-43.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Merged error: 4.0b

Counts

88 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.2b	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (*.f64 a (/.f64 c b)) b)))
5.7b	(*.f64 a (/.f64 c b))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64`
11×	`times-frac_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-r/_binary64` `associate-l*_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/r_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
11.0ms	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (*.f64 a (/.f64 c b)) b)))
8.0ms	(*.f64 a (/.f64 c b))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
120.0ms	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (*.f64 a (/.f64 c b)) b)))
33.0ms	(*.f64 a (/.f64 c b))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5023	1393

prune107.0ms

Filtered

66 candidates to 94 candidates (-42.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	95	5	100

Merged error: 3.4b

Counts

100 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
31.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
11×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `cube-div_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `pow1/3_binary64` `sqr-pow_binary64` `distribute-lft-out--_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 73

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
7.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) 3))

series461.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
109.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
108.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
122.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4978	1860
1	4978	1860

prune111.0ms

Filtered

61 candidates to 85 candidates (-39.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 3.4b

Counts

90 → 5

regimes132.0ms

Accuracy

94.7% (1.0b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 24.8b

bsearch122.0ms

Steps

Iters	Range	Point
7	6.619721456396287e+132	5.15951319309874e+134	1.575494962430441e+134
9	-4.904242864590525e-284	-8.038429285003733e-292	-8.240572048097193e-292
9	-4.2433681095045904e+167	-7.7824311504020155e+158	-7.906974219198102e+158

Iters

Range

Point

6.619721456396287e+132

5.15951319309874e+134

1.575494962430441e+134

-4.904242864590525e-284

-8.038429285003733e-292

-8.240572048097193e-292

-4.2433681095045904e+167

-7.7824311504020155e+158

-7.906974219198102e+158

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	159	238
1	159	238

end0.0ms

sample939.0ms

Algorithm

intervals

Results

652.0ms	8000×	body	128	valid
52.0ms	641×	body	128	nan
33.0ms	398×	body	128	invalid

Details

analyze491.0ms

sample35.0ms

simplify324.0ms

prune5.0ms

localize21.0ms

rewrite26.0ms

series481.0ms

simplify70.0ms

prune117.0ms

localize23.0ms

rewrite32.0ms

series408.0ms

simplify39.0ms

prune107.0ms

localize25.0ms

rewrite34.0ms

series380.0ms

simplify56.0ms

prune107.0ms

localize27.0ms

rewrite28.0ms

series461.0ms

simplify50.0ms

prune111.0ms

regimes132.0ms

bsearch122.0ms

simplify5.0ms

end0.0ms

sample939.0ms

Profiling