Details

sample327.0ms

Algorithm

intervals

Results

8.0ms	196×	body	80	valid
8.0ms	33×	body	2560	valid
6.0ms	24×	body	1280	valid
4.0ms	87×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 33.2b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.4b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

11.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
39.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify140.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune404.0ms

Filtered

92 candidates to 69 candidates (25.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 6.4b

Counts

93 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
39.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	564	2096
1	2553	1897
2	5001	1761

prune540.0ms

Filtered

174 candidates to 86 candidates (50.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	173	9	182

Merged error: 6.3b

Counts

182 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-l`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `diff-log` `associate-*r/` `div-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b_2 b_2) (* a c))
182.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
86.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	397	791
1	1573	705
2	5002	697

prune373.0ms

Filtered

100 candidates to 72 candidates (28.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	100	9	109

Merged error: 6.3b

Counts

109 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `sum-log` `add-cbrt-cube` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 60

Calls

4 calls:

7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
85.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	205	516
1	740	480
2	2640	460
3	5002	456

prune257.0ms

Filtered

72 candidates to 60 candidates (16.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Merged error: 6.3b

Counts

81 → 9

regimes324.0ms

Accuracy

87.1% (3.7b remaining)

Error of 9.3b against oracle of 5.6b and baseline of 34.5b

bsearch170.0ms

Steps

Iters	Range		Point
9	5.514542683406611e+77	2.3545344307669661e+86	6.682995118770345e+77
9	4.002345360978637e-156	6.88386589388666e-150	7.386415230288803e-155
5	-1.3813570841381999e+75	-4.543022443046418e+74	-1.1876632617279024e+75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	24
1	43	24
2	43	24

end0.0ms

sample1.3s

Algorithm

intervals

Results

256.0ms	1060×	body	2560	valid
244.0ms	5862×	body	80	valid
176.0ms	906×	body	1280	valid
114.0ms	2903×	body	80	nan
72.0ms	467×	body	640	valid
34.0ms	112×	body	5120	valid
26.0ms	228×	body	320	valid
8.0ms	104×	body	160	valid

Details

sample327.0ms

simplify13.0ms

prune6.0ms

localize32.0ms

rewrite31.0ms

series354.0ms

simplify140.0ms

prune404.0ms

localize9.0ms

rewrite37.0ms

series384.0ms

simplify71.0ms

prune540.0ms

localize9.0ms

rewrite32.0ms

series386.0ms

simplify46.0ms

prune373.0ms

localize14.0ms

rewrite24.0ms

series324.0ms

simplify75.0ms

prune257.0ms

regimes324.0ms

bsearch170.0ms

simplify2.0ms

end0.0ms

sample1.3s

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