Details

sample37.0ms

Algorithm

intervals

Results

16.0ms	278×	body	80	valid
5.0ms	97×	body	80	nan

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18

prune3.0ms

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: 20.2b

Counts

2 → 1

localize124.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	406	2988
1	1431	1956
2	5002	1869

prune428.0ms

Filtered

152 candidates to 80 candidates (52.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	142	10	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	10	153

Merged error: 8.4b

Counts

153 → 10

localize123.0ms

Local error

Found 4 expressions with local error:

12.7b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 88

Calls

4 calls:

5.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify177.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	283	1391
1	998	1121
2	4723	1013
3	5001	1013

prune466.0ms

Filtered

100 candidates to 83 candidates (83.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	101	9	110

Merged error: 8.4b

Counts

110 → 9

localize123.0ms

Local error

Found 4 expressions with local error:

9.4b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

4 → 76

Calls

4 calls:

5.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify124.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	249	756
1	969	641
2	4038	626
3	5001	624

prune440.0ms

Filtered

88 candidates to 79 candidates (89.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	89	8	97

Merged error: 8.4b

Counts

97 → 8

localize125.0ms

Local error

Found 4 expressions with local error:

23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.8b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.8b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 64

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
142.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify85.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	215	636
1	688	602
2	2689	596
3	5001	594

prune507.0ms

Filtered

76 candidates to 68 candidates (89.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	76	8	84

Merged error: 8.4b

Counts

84 → 8

regimes269.0ms

Accuracy

92.5% (0.9b remaining)

Error of 8.5b against oracle of 7.6b and baseline of 19.5b

bsearch224.0ms

Steps

Iters	Range		Point
8	4.088553977120381e+100	8.044751807128501e+103	6.762593965606264e+103
6	-1.2994787762702041e+157	-3.0529494422842112e+156	-3.0812943354752785e+156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	68
1	57	68

end0.0ms

sample902.0ms

Algorithm

intervals

Results

486.0ms	8757×	body	80	valid
145.0ms	2939×	body	80	nan