Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	40×	body	2560	valid
9.0ms	183×	body	80	valid
7.0ms	25×	body	640	valid
6.0ms	27×	body	1280	valid
4.0ms	93×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	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: 35.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
23.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune257.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	9	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	9	103

Merged error: 3.4b

Counts

103 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 3.0 a) c))
4.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.1b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
144.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
173.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify133.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	669	2663
1	3431	2412
2	5001	2406

prune448.0ms

Filtered

170 candidates to 117 candidates (68.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	168	11	179

Merged error: 3.4b

Counts

179 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 3.0 a) c))
4.7b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
9.1b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
23.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
14.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 3.0 a) c))
147.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
175.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify134.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	714	2019
1	4679	1554
2	5001	1549

prune293.0ms

Filtered

132 candidates to 91 candidates (68.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	2	7	9
Picked	0	1	1
Done	1	0	1
Total	133	10	143

Merged error: 3.4b

Counts

143 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 3.0 a) c))
4.7b	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
9.1b	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
29×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `associate-/r/`
9×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`distribute-rgt-neg-in` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 140

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
12.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 3.0 a) c))
140.0ms	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
175.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	642	2034
1	3061	1813
2	5002	1789

prune320.0ms

Filtered

152 candidates to 108 candidates (71.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	7	8
Picked	1	0	1
Done	1	0	1
Total	154	8	162

Merged error: 3.4b

Counts

162 → 8

regimes357.0ms

Accuracy

90.2% (2.6b remaining)

Error of 8.2b against oracle of 5.5b and baseline of 32.5b

bsearch181.0ms

Steps

Iters	Range		Point
10	1.100420074551047e-18	0.0163835844060345	8.37903889759168e-06
7	-4.075100890035593e-239	-7.186026749476536e-241	-1.1994977793869009e-240
9	-2.697228385254691e+105	-3.334524116472281e+99	-2.2935753422547666e+102

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	27
1	46	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

319.0ms	1087×	body	2560	valid
286.0ms	5798×	body	80	valid
207.0ms	881×	body	1280	valid
138.0ms	2960×	body	80	nan
85.0ms	443×	body	640	valid
44.0ms	118×	body	5120	valid
33.0ms	240×	body	320	valid
12.0ms	133×	body	160	valid