Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	186×	body	80	valid
8.0ms	33×	body	2560	valid
5.0ms	28×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	6×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

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:

64.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
10.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune288.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 232

Calls

4 calls:

29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
55.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
157.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
183.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	829	5121
1	3763	3863
2	5001	3860

prune560.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0b	(/ (* 2.0 a) (* 4.0 (* a c)))
22.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
51×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
34×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`neg-mul-1`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 150

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	610	3042
1	3078	1945
2	5002	1857

prune321.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-exp-log`
166×	`div-exp`
119×	`prod-exp`
65×	`add-sqr-sqrt`
64×	`*-un-lft-identity` `1-exp`
61×	`prod-diff`
60×	`add-cube-cbrt` `add-cbrt-cube`
34×	`rec-exp` `sqrt-prod`
31×	`times-frac`
26×	`cbrt-undiv`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`cbrt-unprod`
14×	`associate-/r/`
13×	`associate-/l*`
11×	`frac-times` `fma-neg`
10×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`neg-mul-1` `associate-*l/`
5×	`pow1` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log` `un-div-inv` `div-inv`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 259

Calls

4 calls:

66.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
31.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1354	4924
1	5002	3462

prune396.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.1b

regimes193.0ms

Accuracy

94.3% (1.4b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 29.6b

bsearch157.0ms

Steps

Iters	Range	Point
7	7.363656180201337e+60	1.0503009045500217e+63	1.0273828621120979e+63
8	-4.3329860630795565e-185	-1.209307133318773e-187	-3.3193805664383666e-186
7	-2.3419197238566892e+109	-5.519096697972622e+107	-2.2237630570465103e+109

Iters

Range

Point

7.363656180201337e+60

1.0503009045500217e+63

1.0273828621120979e+63

-4.3329860630795565e-185

-1.209307133318773e-187

-3.3193805664383666e-186

-2.3419197238566892e+109

-5.519096697972622e+107

-2.2237630570465103e+109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	37
1	47	37

end0.0ms

sample1.2s

Algorithm

intervals

Results

228.0ms	5865×	body	80	valid
226.0ms	1052×	body	2560	valid
161.0ms	932×	body	1280	valid
105.0ms	2817×	body	80	nan
61.0ms	453×	body	640	valid
29.0ms	113×	body	5120	valid
24.0ms	235×	body	320	valid
10.0ms	120×	body	160	valid