Details

Time bar (total: 6.0s)

sample42.0ms

Algorithm
intervals
Results
8.0ms185×body80valid
7.0ms30×body2560valid
5.0ms25×body1280valid
4.0ms99×body80nan
3.0ms20×body640valid
1.0ms5×body5120valid
1.0ms6×body320valid
0.0ms5×body160valid

simplify11.0ms

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: 36.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite54.0ms

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:
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
2.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0405779
11563685
25001674

prune234.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
3.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(/ (/ (+ 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)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06402579
131552333
250012320

prune428.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b
(- (* b b) (* (* 4.0 a) c))
14.6b
(/ (* 2.0 a) (* 4.0 (* a c)))
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
123×add-exp-log
63×add-cbrt-cube
57×prod-exp
40×div-exp
25×cbrt-unprod
20×cbrt-undiv
8×pow1 add-sqr-sqrt rec-exp 1-exp
7×add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×associate-/r/
4×flip3-- times-frac flip-- associate-/l*
3×sqrt-prod
2×frac-times pow-flip frac-2neg sqrt-div associate-*r/ clear-num associate-/r* div-inv
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down associate-*l/ inv-pow
Counts
4 → 109
Calls
4 calls:
66.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07101430
142771093
250021071

prune249.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
0.8b
(- (* b b) (* (* 4.0 a) c))
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
1901×times-frac
815×add-sqr-sqrt
814×*-un-lft-identity
810×add-cube-cbrt
102×div-inv
87×add-exp-log
70×div-exp
44×associate-/l*
25×add-cbrt-cube
15×cbrt-undiv rec-exp 1-exp associate-/r/
13×associate-/r*
10×add-log-exp
5×pow1
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 720
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
51.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify150.0ms

Algorithm
egg-herbie
Counts
732 → 732
Iterations

Useful iterations: 1 (63.0ms)

IterNodesCost
039619260
150018103

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.6b

regimes186.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.5b

bsearch175.0ms

Steps
ItersRangePoint
7
6.714891876596302e+121
1.686395921989292e+123
2.1125387673008883e+122
10
-5.399505147647774e-194
-1.4984247517127078e-204
-3.27314384198807e-203
4
-1.078360482931843e+145
-7.501243017467935e+144
-7.603816824088264e+144

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04735
14735

end0.0ms

sample1.2s

Algorithm
intervals
Results
262.0ms1083×body2560valid
243.0ms5894×body80valid
175.0ms896×body1280valid
113.0ms2938×body80nan
68.0ms438×body640valid
36.0ms117×body5120valid
26.0ms229×body320valid
8.0ms100×body160valid