Details

sample62.0ms

Algorithm

intervals

Results

13.0ms	31×	body	2560	valid
10.0ms	203×	body	80	valid
5.0ms	24×	body	1280	valid
4.0ms	78×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	13
1	42	13

prune5.0ms

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: 32.5b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5271	1600

prune160.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Merged error: 6.2b

Counts

104 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

15.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
15.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5017	3712

prune169.0ms

Filtered

102 candidates to 189 candidates (-85.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	191	9	200

Merged error: 6.1b

Counts

200 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.5b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0b	(/ (* a c) a)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
3×	`times-frac` `associate-/r*` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `sqrt-div` `div-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` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 63

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(/ (* a c) a)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4989	648
1	4989	648

prune109.0ms

Filtered

57 candidates to 75 candidates (-31.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	74	10	84

Merged error: 6.1b

Counts

84 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

10.0ms	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4941	1197
1	4941	1197

prune86.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	92	9	101

Merged error: 6.1b

Counts

101 → 9

regimes320.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.8b

bsearch117.0ms

Steps

Iters	Range	Point
10	1.1487243557305423e+102	3.920821933018458e+112	9.421054264015979e+109
9	4.8461344139268896e-188	1.768914724278288e-182	4.8980015245867535e-188
10	-8.003596903883499e+165	-5.641302321031635e+152	-8.411718004910904e+153

Iters

Range

Point

1.1487243557305423e+102

3.920821933018458e+112

9.421054264015979e+109

4.8461344139268896e-188

1.768914724278288e-182

4.8980015245867535e-188

-8.003596903883499e+165

-5.641302321031635e+152

-8.411718004910904e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	58
1	39	58

end0.0ms

sample1.6s

Algorithm

intervals

Results

297.0ms	1062×	body	2560	valid
287.0ms	5949×	body	80	valid
191.0ms	856×	body	1280	valid
145.0ms	2987×	body	80	nan
81.0ms	460×	body	640	valid
41.0ms	117×	body	5120	valid
31.0ms	232×	body	320	valid
10.0ms	112×	body	160	valid

Details

sample62.0ms

simplify8.0ms

prune5.0ms

localize21.0ms

rewrite36.0ms

series70.0ms

simplify52.0ms

prune160.0ms

localize11.0ms

rewrite45.0ms

series70.0ms

simplify69.0ms

prune169.0ms

localize11.0ms

rewrite26.0ms

series39.0ms

simplify40.0ms

prune109.0ms

localize9.0ms

rewrite29.0ms

series92.0ms

simplify42.0ms

prune86.0ms

regimes320.0ms

bsearch117.0ms

simplify1.0ms

end0.0ms

sample1.6s

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