Details

Time bar (total: 7.4s)

sample118.0ms

Algorithm
intervals
Results
28.0ms130×body320valid
24.0ms288×body80nan
21.0ms544×pre80true
17.0ms91×body160valid
3.0ms12×body640valid
2.0ms23×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize12.0ms

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))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25002674

prune188.0ms

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)))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 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 → 151
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
156.0ms
(/ (/ (+ 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)))))

simplify116.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06422664
131752400
250032388

prune421.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.5b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
166×add-sqr-sqrt
138×times-frac
96×*-un-lft-identity
60×difference-of-squares
56×add-cube-cbrt
52×cbrt-prod
50×sqrt-prod
42×associate-/l*
20×distribute-lft-out--
19×add-exp-log add-cbrt-cube
16×unpow-prod-down cube-prod
12×associate-/r* sqr-pow
10×distribute-rgt-neg-in
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×cube-div div-inv add-log-exp
3×pow-unpow associate-/l/
2×cube-mult cbrt-div frac-2neg unpow3 prod-exp clear-num cbrt-unprod
1×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 209
Calls
4 calls:
89.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
5.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
5.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series494.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
190.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
52.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
98.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify158.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
08564206
144263827
250013808

prune618.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (- (* b b) (* (* 4.0 a) c)) 3/2)
0.4b
(pow (- (* b b) (* (* 4.0 a) c)) 3/2)
0.4b
(* (pow (- (* b b) (* (* 4.0 a) c)) 3/2) (pow (- (* b b) (* (* 4.0 a) c)) 3/2))
0.5b
(cbrt (* (pow (- (* b b) (* (* 4.0 a) c)) 3/2) (pow (- (* b b) (* (* 4.0 a) c)) 3/2)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×unpow-prod-down
18×add-exp-log
16×add-cube-cbrt *-un-lft-identity
12×sqr-pow
9×prod-exp unswap-sqr
8×pow-to-exp pow-exp
7×swap-sqr associate-*r* associate-*l*
6×pow1 pow-unpow add-cbrt-cube
4×add-log-exp
2×pow-pow
1×cbrt-prod pow2 pow1/3 pow-prod-down pow-sqr *-commutative pow-prod-up cbrt-unprod
Counts
4 → 95
Calls
4 calls:
8.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3/2)
4.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3/2)
33.0ms
(* (pow (- (* b b) (* (* 4.0 a) c)) 3/2) (pow (- (* b b) (* (* 4.0 a) c)) 3/2))
10.0ms
(cbrt (* (pow (- (* b b) (* (* 4.0 a) c)) 3/2) (pow (- (* b b) (* (* 4.0 a) c)) 3/2)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3/2)
77.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3/2)
98.0ms
(* (pow (- (* b b) (* (* 4.0 a) c)) 3/2) (pow (- (* b b) (* (* 4.0 a) c)) 3/2))
48.0ms
(cbrt (* (pow (- (* b b) (* (* 4.0 a) c)) 3/2) (pow (- (* b b) (* (* 4.0 a) c)) 3/2)))

simplify48.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
02501073
11162874
25001840

prune331.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
13121
23121

end0.0ms

sample3.2s

Algorithm
intervals
Results
817.0ms3664×body320valid
679.0ms8118×body80nan
599.0ms16118×pre80true
459.0ms2949×body160valid
150.0ms507×body640valid
78.0ms880×body80valid