Details

sample48.0ms

Algorithm

intervals

Results

9.0ms	201×	body	80	valid
9.0ms	24×	body	2560	valid
6.0ms	26×	body	1280	valid
4.0ms	97×	body	80	nan
2.0ms	13×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

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:

66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

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

prune390.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

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

Counts

4 → 69

Calls

4 calls:

43.0ms	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
40.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	370	755
1	1529	656
2	5001	644

prune395.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

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`
8×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
5×	`distribute-rgt-neg-in` `associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `neg-log` `clear-num` `div-inv` `inv-pow`

Counts

4 → 83

Calls

4 calls:

41.0ms	(/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	359	904
1	1455	811
2	5001	778

prune419.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite64.0ms

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:

23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
62.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	217	598
1	808	556
2	3289	534
3	5001	530

prune533.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.1b

regimes281.0ms

Accuracy

89% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 34.8b

bsearch219.0ms

Steps

Iters	Range		Point
10	3.61186574816217e+49	1.3635073763102398e+60	2.401197553364029e+58
6	2.8042826217254478e-101	1.1404586743069836e-100	2.826972719711758e-101
5	-1.1878056610710861e+97	-3.0473552791360753e+96	-4.1614218427535572e+96

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	33
1	55	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

291.0ms	1081×	body	2560	valid
267.0ms	5776×	body	80	valid
205.0ms	912×	body	1280	valid
136.0ms	3053×	body	80	nan
83.0ms	483×	body	640	valid
40.0ms	268×	body	320	valid
39.0ms	114×	body	5120	valid
9.0ms	103×	body	160	valid