Details

Time bar (total: 8.0s)

sample111.0ms

Algorithm
intervals
Results
27.0ms130×body320valid
25.0ms288×body80nan
20.0ms544×pre80true
13.0ms91×body160valid
3.0ms12×body640valid
2.0ms23×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: 54.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

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)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
32.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms
(+ (- 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)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25002735

prune233.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite97.0ms

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:
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
25.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series471.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(- (* b b) (* (* 4.0 a) c))
141.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
185.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify145.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
08325100
139673830
250013828

prune535.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize27.0ms

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))))))
0.3b
(* (* a c) (fma b b (* (* 4.0 a) c)))
0.4b
(/ (- (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)

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
58×*-un-lft-identity times-frac
36×difference-of-squares
34×add-cube-cbrt
21×sqr-pow
19×add-exp-log add-cbrt-cube
15×pow1
13×associate-/l*
12×distribute-lft-out--
11×associate-/r*
9×unpow-prod-down
8×sqrt-prod
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u associate-/l/ add-log-exp
3×pow-unpow pow-pow associate-*r* pow-exp rem-cube-cbrt
2×cbrt-undiv flip3-- frac-2neg div-exp 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 → 162
Calls
4 calls:
88.0ms
(/ (+ 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))))))
6.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
29.0ms
(/ (- (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
(pow (* (* 4.0 a) c) 3)

series523.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(/ (+ 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))))))
63.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
131.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
59.0ms
(pow (* (* 4.0 a) c) 3)

simplify148.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
07553316
137703092
250013091

prune792.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 1 (/ (* 4.0 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))))) c))) (* 2.0 a))
0.3b
(* (* a c) (fma b b (* (* 4.0 a) c)))
0.4b
(/ (- (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)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
114×add-exp-log
73×add-cbrt-cube
49×add-sqr-sqrt
47×div-exp
45×prod-exp
31×times-frac
29×*-un-lft-identity
26×cbrt-unprod
25×cbrt-undiv
24×difference-of-squares
21×add-cube-cbrt sqr-pow
15×pow1
11×associate-/l*
10×1-exp
9×unpow-prod-down
6×pow-prod-down
4×expm1-log1p-u associate-/r* log1p-expm1-u distribute-lft-out-- add-log-exp
3×pow-unpow pow-pow associate-*r* pow-exp associate-/l/ rem-cube-cbrt
2×frac-2neg clear-num fma-udef div-inv
1×distribute-rgt-in cube-mult pow-to-exp flip3-- distribute-lft-in unpow3 div-sub cube-prod associate-*r/ associate-*l* *-commutative flip--
Counts
4 → 159
Calls
4 calls:
50.0ms
(/ (* 1 (/ (* 4.0 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))))) c))) (* 2.0 a))
9.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
29.0ms
(/ (- (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
(pow (* (* 4.0 a) c) 3)

series480.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (* 1 (/ (* 4.0 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))))) c))) (* 2.0 a))
59.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
133.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
53.0ms
(pow (* (* 4.0 a) c) 3)

simplify55.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010023335
150012709

prune627.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes95.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03622
13822
23822

end0.0ms

sample3.0s

Algorithm
intervals
Results
769.0ms3664×body320valid
620.0ms8118×body80nan
572.0ms16118×pre80true
433.0ms2949×body160valid
141.0ms507×body640valid
74.0ms880×body80valid