Details

sample85.0ms

Algorithm

intervals

Results

18.0ms	209×	body	80	valid
13.0ms	32×	body	1280	valid
12.0ms	25×	body	2560	valid
8.0ms	103×	body	80	nan
5.0ms	14×	body	640	valid
4.0ms	4×	body	320	valid
2.0ms	4×	body	5120	valid
0.0ms	1×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 28.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(- (* b b) (* (* 3.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
58.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune210.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 3.6b

Counts

83 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
0.4b	(- (* b b) (* (* 3.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt`
4×	`div-exp`
3×	`times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `flip3--` `pow-flip` `sqrt-div` `1-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `neg-log` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 70

Calls

4 calls:

4.0ms	(/ 1 (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (* 3.0 a))
45.0ms	(- (* b b) (* (* 3.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	338	493
1	1380	446
2	5001	430

prune170.0ms

Filtered

82 candidates to 55 candidates (67.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	82	12	94

Merged error: 3.6b

Counts

94 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(- (* b b) (* (* 3.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

14.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
48.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
66.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	368	755
1	1544	656
2	5002	644

prune190.0ms

Filtered

81 candidates to 61 candidates (75.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	80	13	93

Merged error: 3.5b

Counts

93 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
5.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
49.0ms	(- (* b b) (* (* 3.0 a) c))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune151.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	72	13	85

Merged error: 3.5b

Counts

85 → 13

regimes412.0ms

Accuracy

88.3% (3.3b remaining)

Error of 9.0b against oracle of 5.7b and baseline of 33.9b

bsearch215.0ms

Steps

Iters	Range	Point
9	1.7536266209730185e+54	9.156208036690931e+61	3.608927477968443e+61
10	2.5315207871164436e-148	2.951160339144991e-136	1.5652193548450996e-141
9	-1.5770435612361704e+159	-6.635354719968133e+153	-1.2515051492553303e+154

Iters

Range

Point

1.7536266209730185e+54

9.156208036690931e+61

3.608927477968443e+61

2.5315207871164436e-148

2.951160339144991e-136

1.5652193548450996e-141

-1.5770435612361704e+159

-6.635354719968133e+153

-1.2515051492553303e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	30
1	53	30
2	53	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

304.0ms	1054×	body	2560	valid
286.0ms	5867×	body	80	valid
207.0ms	896×	body	1280	valid
145.0ms	2925×	body	80	nan
86.0ms	459×	body	640	valid
35.0ms	104×	body	5120	valid
30.0ms	218×	body	320	valid
10.0ms	107×	body	160	valid