Details

Time bar (total: 4.7s)

sample285.0ms

Algorithm
intervals
Results
7.0ms35×body2560valid
7.0ms197×body80valid
4.0ms90×body80nan
4.0ms28×body1280valid
2.0ms13×body640valid
1.0ms11×body320valid
0.0ms2×body5120valid
0.0ms2×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
46.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms
(- (* b_2 b_2) (* a c))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0389850
11366779
25001753

prune299.0ms

Filtered
112 candidates to 88 candidates (78.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.7b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 210
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
41.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
142.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
169.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify120.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
07613434
134903258
250023250

prune520.0ms

Filtered
222 candidates to 152 candidates (68.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
12.1b
(/ a (* a c))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- times-frac diff-log flip-- associate-/l*
2×cbrt-undiv sub-neg sqrt-div div-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 146
Calls
4 calls:
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
3.0ms
(/ a (* a c))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series171.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(/ a (* a c))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04732541
116081646
250011557

prune271.0ms

Filtered
158 candidates to 80 candidates (50.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
39×add-exp-log
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×div-exp
13×add-cbrt-cube
12×prod-exp
11×fma-neg
10×add-log-exp
8×pow1 rec-exp 1-exp
7×neg-mul-1
5×flip3-- associate-/r/ flip--
4×cbrt-undiv expm1-log1p-u log1p-expm1-u
3×times-frac diff-log associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 168
Calls
4 calls:
29.0ms
(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms
(- (- 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)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify82.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06222950
124621917
250011869

prune277.0ms

Filtered
180 candidates to 89 candidates (49.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.6b

regimes147.0ms

Accuracy

94% (1.4b remaining)

Error of 6.7b against oracle of 5.2b and baseline of 28.9b

bsearch143.0ms

Steps
ItersRangePoint
9
8.465625442272063e+58
8.825425083170634e+65
5.674292264829422e+63
7
-6.207156945681686e-303
-1.2633929192945347e-304
-1.6070331019441596e-304
10
-5.288637106878427e+83
-2.355035228211621e+66
-2.4276688444363324e+79

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04128
14328
24328

end0.0ms

sample989.0ms

Algorithm
intervals
Results
199.0ms1083×body2560valid
187.0ms5784×body80valid
148.0ms926×body1280valid
94.0ms2977×body80nan
53.0ms453×body640valid
27.0ms106×body5120valid
23.0ms258×body320valid
10.0ms119×body160valid