Details

Time bar (total: 7.0s)

sample58.0ms

Algorithm
intervals
Results
11.0ms148×body160valid
11.0ms552×pre80true
10.0ms296×body80nan
7.0ms108×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: 28.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
28.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite58.0ms

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)))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25001735

prune278.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

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:
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
209.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify153.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
08325099
139673830
250013828

prune601.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))
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)

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
188×add-sqr-sqrt
180×prod-diff
175×sqrt-prod
153×*-un-lft-identity
152×cbrt-prod
133×add-cube-cbrt
62×distribute-rgt-neg-in
57×distribute-lft-neg-in
41×unpow-prod-down cube-prod
33×times-frac
30×difference-of-squares
19×neg-mul-1
17×sqr-pow
12×cube-mult unpow3
11×associate-/r*
10×fma-neg distribute-lft-out--
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1
4×cube-div expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×pow-unpow associate-/l*
2×cbrt-div diff-log associate-/r/ associate-/l/
1×cbrt-undiv associate--l- neg-sub0 pow-to-exp sub-neg pow-pow frac-2neg flip3-+ pow1/3 div-exp neg-log pow-exp clear-num rem-cbrt-cube flip-+ div-inv rem-cube-cbrt
Counts
4 → 331
Calls
4 calls:
33.0ms
(- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))
53.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- 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)

series399.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))
183.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
44.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
94.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify182.0ms

Algorithm
egg-herbie
Counts
343 → 343
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
098810804
138147114
250016932

prune640.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2)))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2))))

rewrite28.0ms

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:
11.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
0.0ms
(fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2)))
7.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2))))

series1.3s

Counts
4 → 12
Calls
4 calls:
513.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2)))) (* 2.0 a))
49.0ms
(- (* b b) (* (* 4.0 a) c))
165.0ms
(fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2)))
611.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2))))

simplify132.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
08502519
140382179
250012177

prune460.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes157.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02816
13016
23016

end0.0ms

sample1.4s

Algorithm
intervals
Results
322.0ms4508×body160valid
315.0ms16623×pre80true
301.0ms8623×body80nan
130.0ms3492×body80valid