Details

sample65.0ms

Algorithm

intervals

Results

13.0ms	35×	body	2560	valid
12.0ms	195×	body	80	valid
10.0ms	33×	body	1280	valid
6.0ms	97×	body	80	nan
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune2.0ms

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: 32.9b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 4.0 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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune218.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 5.8b

Counts

83 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	525	1588
1	2570	1375
2	5001	1308

prune251.0ms

Filtered

126 candidates to 71 candidates (56.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Merged error: 5.7b

Counts

134 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cbrt 1) (cbrt 1)) (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

15.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	519	1272
1	2631	1040
2	5001	949

prune268.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	100	7	107

Merged error: 5.7b

Counts

107 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (* b b) (* (* 4.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	149	476
1	576	446
2	2486	444
3	5001	440

prune220.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	66	7	73

Merged error: 5.7b

Counts

73 → 7

regimes194.0ms

Accuracy

89% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 34.3b

bsearch221.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	1.7408270256230484e+101
10	-3.3872652091741538e-211	-3.093295365731255e-225	-8.781062788627254e-225
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

1.7408270256230484e+101

-3.3872652091741538e-211

-3.093295365731255e-225

-8.781062788627254e-225

-3.0529494422842112e+156

-1.5054982703030158e+138

-2.7863758169125638e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	37
1	57	37

end0.0ms

sample1.2s

Algorithm

intervals

Results

269.0ms	1101×	body	2560	valid
236.0ms	5787×	body	80	valid
170.0ms	900×	body	1280	valid
111.0ms	2923×	body	80	nan
69.0ms	458×	body	640	valid
37.0ms	105×	body	5120	valid
25.0ms	227×	body	320	valid
10.0ms	123×	body	160	valid