Details

Time bar (total: 6.6s)

sample58.0ms

Algorithm
intervals
Results
11.0ms111×body320valid
10.0ms534×pre80true
9.0ms278×body80nan
7.0ms99×body160valid
2.0ms16×body640valid
1.0ms30×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: 52.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
29.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite56.0ms

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)))
35.0ms
(/ (+ (- 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))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25001735

prune263.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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)))))

rewrite105.0ms

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:
17.0ms
(- (- 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))
30.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
189.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify150.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
08325099
139673830
250013828

prune592.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(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)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite26.0ms

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))
0.0ms
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* 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))
8.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series748.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
179.0ms
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
239.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
284.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify114.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
05982143
130141804
250021754

prune448.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))))
0.6b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
19×add-exp-log add-cbrt-cube
16×associate-/l*
12×cbrt-prod
7×cbrt-undiv div-exp
6×unpow-prod-down cube-prod
5×pow1
4×cube-div expm1-log1p-u associate-/r* log1p-expm1-u div-inv add-log-exp
3×pow-unpow associate-/l/
2×cube-mult cbrt-div flip3-- frac-2neg unpow3 prod-exp clear-num flip-- cbrt-unprod sqr-pow
1×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 131
Calls
4 calls:
12.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))) (* 2.0 a))
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))
4.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series659.0ms

Counts
4 → 12
Calls
4 calls:
232.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))) (* 2.0 a))
279.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))))
50.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
97.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify130.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
06742563
136072244
250012239

prune569.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes112.0ms

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
03018
13218
23218

end0.0ms

sample1.6s

Algorithm
intervals
Results
378.0ms3618×body320valid
299.0ms16074×pre80true
264.0ms8074×body80nan
201.0ms2928×body160valid
77.0ms529×body640valid
32.0ms925×body80valid