Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	181×	body	80	valid
6.0ms	33×	body	1280	valid
3.0ms	92×	body	80	nan
2.0ms	17×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

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: 37.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune250.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series654.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
360.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	640	2692
1	2944	2439
2	5001	2426

prune392.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
45×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 114

Calls

4 calls:

15.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
46.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	521	1588
1	2522	1375
2	5002	1308

prune249.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series291.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify110.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	216	561
1	809	538
2	3258	523
3	5001	519

prune267.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.9b

regimes264.0ms

Accuracy

84.5% (4.2b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 33.1b

bsearch101.0ms

Steps

Iters	Range		Point
9	1.4411111155905935e-45	3.477369949839467e-39	4.3062534203630095e-45
5	-2.2693772293991552e+117	-7.333494566860601e+116	-1.5277916383184032e+117

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

254.0ms	1057×	body	2560	valid
241.0ms	5837×	body	80	valid
171.0ms	876×	body	1280	valid
109.0ms	2892×	body	80	nan
68.0ms	459×	body	640	valid
40.0ms	137×	body	5120	valid
27.0ms	245×	body	320	valid
7.0ms	95×	body	160	valid