Details

Time bar (total: 6.9s)

sample58.0ms

Algorithm
intervals
Results
15.0ms159×body160valid
10.0ms504×pre80true
9.0ms248×body80nan
5.0ms46×body320valid
2.0ms51×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite63.0ms

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:
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
40.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0438854
11702750
25002735

prune253.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite106.0ms

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:
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
31.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series454.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify162.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
08325099
139673830
250013828

prune552.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- 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)))))) (* 2.0 a))
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)))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
115×add-sqr-sqrt
114×times-frac
77×*-un-lft-identity
45×add-cube-cbrt
42×difference-of-squares
40×associate-/l*
29×add-exp-log add-cbrt-cube
21×sqr-pow
16×distribute-lft-out--
15×pow1
12×sqrt-prod
9×unpow-prod-down
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×distribute-rgt-neg-in pow-prod-down
4×expm1-log1p-u associate-/r* associate-/r/ log1p-expm1-u div-inv add-log-exp
3×pow-unpow flip3-- pow-pow associate-*r* pow-exp flip-- associate-/l/ rem-cube-cbrt
2×frac-2neg clear-num fma-udef
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative
Counts
4 → 191
Calls
4 calls:
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- 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)))))) (* 2.0 a))
7.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
37.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
7.0ms
(pow (* (* 4.0 a) c) 3)

series482.0ms

Counts
4 → 12
Calls
4 calls:
230.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- 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)))))) (* 2.0 a))
59.0ms
(* (* 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)))
58.0ms
(pow (* (* 4.0 a) c) 3)

simplify158.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09604391
147324015
250014015

prune894.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize27.0ms

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)))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- 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)))))))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
33×times-frac
31×*-un-lft-identity
26×add-exp-log add-cbrt-cube
24×difference-of-squares
23×add-cube-cbrt
21×sqr-pow
15×pow1
13×associate-/l*
9×unpow-prod-down prod-exp cbrt-unprod
6×pow-prod-down
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u associate-/l/ distribute-lft-out-- add-log-exp
3×pow-unpow pow-pow associate-*r* pow-exp rem-cube-cbrt
2×flip3-- frac-2neg associate-*r/ clear-num associate-/r/ flip-- fma-udef div-inv
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in flip3-+ unpow3 div-sub cube-prod associate-*l* *-commutative flip-+
Counts
4 → 138
Calls
4 calls:
7.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
35.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
61.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- 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)))))))
7.0ms
(pow (* (* 4.0 a) c) 3)

series461.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
126.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
221.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- 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)))))))
52.0ms
(pow (* (* 4.0 a) c) 3)

simplify180.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08052573
148092270
250012270

prune657.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
12921

end0.0ms

sample1.5s

Algorithm
intervals
Results
341.0ms4829×body160valid
302.0ms16283×pre80true
279.0ms8283×body80nan
149.0ms1358×body320valid
66.0ms1813×body80valid