Details

Time bar (total: 6.7s)

sample74.0ms

Algorithm
intervals
Results
18.0ms147×body160valid
16.0ms248×body80nan
15.0ms504×pre80true
8.0ms109×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: 29.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite57.0ms

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))
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25002735

prune251.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* 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)))))

rewrite103.0ms

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))
43.0ms
(/ (/ (+ 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)))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(/ (/ (+ 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)))))

simplify160.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
08325099
139673830
250013828

prune537.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
16×associate-/l*
7×cbrt-undiv div-exp
6×add-log-exp
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sub-neg flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ fma-udef
Counts
4 → 105
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
224.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
168.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
267.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify115.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
05982143
130141804
250021754

prune408.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (sqrt b) (- (sqrt b)) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt 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)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×cbrt-prod
9×times-frac
7×add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
5×pow1
4×cube-div expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* associate-/l*
2×cube-mult cbrt-div flip3-- unpow3 flip-- associate-/l/ sqr-pow
1×cbrt-undiv pow-to-exp pow-pow frac-2neg flip3-+ pow1/3 div-exp pow-exp clear-num rem-cbrt-cube flip-+ fma-udef div-inv rem-cube-cbrt
Counts
4 → 93
Calls
4 calls:
0.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
8.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))))
4.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
5.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series558.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
260.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))))
46.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
90.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify93.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
05021444
125211270
250011231

prune350.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes95.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03018
13218
23218

end0.0ms

sample2.2s

Algorithm
intervals
Results
562.0ms4421×body160valid
548.0ms8591×body80nan
486.0ms16591×pre80true
255.0ms3579×body80valid