Details

Time bar (total: 7.3s)

sample61.0ms

Algorithm
intervals
Results
12.0ms112×body320valid
10.0ms537×pre80true
10.0ms281×body80nan
7.0ms92×body160valid
2.0ms15×body640valid
1.0ms37×body80valid

simplify11.0ms

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: 50.9b

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))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite33.0ms

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)))
4.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
42.0ms
(- (* 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))))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25002735

prune248.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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

rewrite53.0ms

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:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
144.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
179.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify181.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (146.0ms)

IterNodesCost
08325099
139673830
250013828

prune543.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize33.0ms

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))))))
0.4b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
0.4b
(* (* a c) (fma b b (* (* 4.0 a) c)))
0.8b
(pow (* (* 4.0 a) c) 3)

rewrite64.0ms

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:
29.0ms
(/ (+ 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))))))
14.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
5.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
6.0ms
(pow (* (* 4.0 a) c) 3)

series514.0ms

Counts
4 → 12
Calls
4 calls:
273.0ms
(/ (+ 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))))))
125.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
64.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
52.0ms
(pow (* (* 4.0 a) c) 3)

simplify153.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
07553316
137703092
250013091

prune791.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (/ (- (- 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))))) (* 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)))
0.4b
(* (* a c) (fma b b (* (* 4.0 a) c)))
0.8b
(pow (* (* 4.0 a) c) 3)

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
402×times-frac
250×add-sqr-sqrt
194×*-un-lft-identity
138×add-cube-cbrt
60×difference-of-squares
51×add-exp-log
43×associate-/r*
31×add-cbrt-cube
28×distribute-lft-out--
24×div-exp sqrt-prod
21×sqr-pow
18×div-inv
16×pow1
13×associate-/l*
12×distribute-rgt-neg-in
10×cbrt-undiv
9×unpow-prod-down prod-exp
7×cbrt-unprod
6×pow-prod-down
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×pow-unpow pow-pow associate-*r* pow-exp rem-cube-cbrt
2×frac-2neg clear-num fma-udef associate-/l/
1×distribute-rgt-in cube-mult pow-to-exp flip3-- pow-flip distribute-lft-in unpow3 div-sub cube-prod associate-*l* associate-/r/ *-commutative flip-- inv-pow
Counts
4 → 303
Calls
4 calls:
39.0ms
(/ 1 (/ (/ (- (- 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))))) (* 4.0 a)) c))
14.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
5.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
6.0ms
(pow (* (* 4.0 a) c) 3)

series525.0ms

Counts
4 → 12
Calls
4 calls:
274.0ms
(/ 1 (/ (/ (- (- 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))))) (* 4.0 a)) c))
128.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
64.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
59.0ms
(pow (* (* 4.0 a) c) 3)

simplify103.0ms

Algorithm
egg-herbie
Counts
315 → 315
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013908147
150017608

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes116.0ms

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
03522
13722
23722

end0.0ms

sample1.7s

Algorithm
intervals
Results
407.0ms3660×body320valid
311.0ms16233×pre80true
289.0ms8233×body80nan
221.0ms2937×body160valid
77.0ms497×body640valid
37.0ms906×body80valid