Details

Time bar (total: 4.5s)

sample56.0ms

Algorithm
intervals
Results
15.0ms39×body2560valid
13.0ms209×body80valid
6.0ms107×body80nan
5.0ms21×body1280valid
2.0ms10×body640valid
1.0ms4×body320valid
0.0ms3×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
35.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
66.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms
(- (* b_2 b_2) (* a c))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify38.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0368965
11241910
25001901

prune220.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
130×add-sqr-sqrt
129×*-un-lft-identity
77×add-cube-cbrt
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×flip3-- div-exp flip--
6×pow1
5×div-inv
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 177
Calls
4 calls:
28.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
66.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms
(- (* b_2 b_2) (* a c))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05912458
127062226
250012071

prune271.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×add-exp-log add-cube-cbrt associate-*l*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg prod-exp distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in sqrt-div associate-*r/ div-exp cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 92
Calls
4 calls:
50.0ms
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms
(- (* b_2 b_2) (* a c))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0428897
11762804
25001786

prune207.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
1.6b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0b
(/ (+ 0 (* a c)) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1
3×flip3-+ times-frac sqrt-prod flip-+ associate-/l*
2×cbrt-undiv flip3-- sqrt-div associate-*r/ div-exp sum-log associate-/r/ flip-- associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 67
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(/ (+ 0 (* a c)) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
147.0ms
(/ (+ 0 (* a c)) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
55.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify84.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0429703
12181598
25001587

prune236.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.5b

regimes198.0ms

Accuracy

90.8% (2.6b remaining)

Error of 8.2b against oracle of 5.6b and baseline of 34.1b

bsearch130.0ms

Steps
ItersRangePoint
6
5.779436182351587e+124
6.964873849469576e+125
4.833109120774969e+125
7
2.0861158575113534e-296
5.236994814729212e-295
2.329606077024855e-296
7
-2.3860448187824777e+68
-1.0929352752278947e+66
-2.4834941205945284e+67

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04224
14224

end0.0ms

sample1.6s

Algorithm
intervals
Results
397.0ms5956×body80valid
350.0ms1053×body2560valid
253.0ms905×body1280valid
166.0ms2823×body80nan
97.0ms447×body640valid
41.0ms102×body5120valid
32.0ms195×body320valid
14.0ms103×body160valid