Details

Time bar (total: 6.6s)

sample54.0ms

Algorithm
intervals
Results
13.0ms540×pre80true
10.0ms146×body160valid
9.0ms284×body80nan
4.0ms110×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
28.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite30.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25001735

prune270.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×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
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
11.0ms
(- (- 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))
4.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
48.0ms
(- (* b b) (* (* 4.0 a) c))
186.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify157.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
08325099
139673830
250013828

prune574.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1)))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u
3×associate-/r* associate-/l*
2×sub-neg flip3-- flip3-+ fma-neg diff-log prod-diff associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 75
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(- (* b b) (* (* 4.0 a) c))
1.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
7.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1)))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(- (* b b) (* (* 4.0 a) c))
175.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
278.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1)))))

simplify91.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
04261761
121701592
250011573

prune466.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* a c) (fma b b (* (* 4.0 a) c)))
0.3b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1)))))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
39×times-frac
37×*-un-lft-identity
29×add-cube-cbrt
24×difference-of-squares
21×sqr-pow
19×add-exp-log add-cbrt-cube
15×pow1
13×associate-/l*
9×unpow-prod-down
6×pow-prod-down prod-exp associate-/r* cbrt-unprod
4×expm1-log1p-u log1p-expm1-u associate-/l/ distribute-lft-out-- add-log-exp
3×pow-unpow pow-pow associate-*r* pow-exp rem-cube-cbrt
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+ fma-udef div-inv
1×distribute-rgt-in cube-mult pow-to-exp flip3-- distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative flip--
Counts
4 → 142
Calls
4 calls:
5.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
15.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
6.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1)))))
6.0ms
(pow (* (* 4.0 a) c) 3)

series621.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
135.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
373.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1)))))
54.0ms
(pow (* (* 4.0 a) c) 3)

simplify158.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (123.0ms)

IterNodesCost
07613444
137893176
250013174

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes146.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05137
15537
25537

end0.0ms

sample1.4s

Algorithm
intervals
Results
312.0ms4486×body160valid
306.0ms16546×pre80true
283.0ms8546×body80nan
125.0ms3514×body80valid