Details

Time bar (total: 7.8s)

sample77.0ms

Algorithm
intervals
Results
18.0ms185×body80valid
14.0ms30×body2560valid
10.0ms25×body1280valid
9.0ms99×body80nan
7.0ms20×body640valid
3.0ms5×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify13.0ms

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: 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)))

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:
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0438855
11702750
25001735

prune319.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize20.0ms

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×expm1-log1p-u log1p-expm1-u 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 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
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))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
154.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
194.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify125.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
06742663
134622412
250012406

prune527.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ 1 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)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
283×add-exp-log
136×div-exp
121×prod-exp
109×add-cbrt-cube
42×cbrt-undiv
41×cbrt-unprod
40×1-exp
32×times-frac
20×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
16×rec-exp
14×associate-/l*
6×add-log-exp
5×pow1 associate-/r/
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×sqrt-prod
2×frac-times frac-2neg sqrt-div associate-*r/ clear-num associate-/r*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-*l/ associate-/l/
Counts
4 → 177
Calls
4 calls:
40.0ms
(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011152569
150012001

prune371.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize16.0ms

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)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
1901×times-frac
856×add-sqr-sqrt
855×*-un-lft-identity
851×add-cube-cbrt
102×div-inv
87×add-exp-log
70×div-exp
61×prod-diff
44×associate-/l*
34×sqrt-prod
25×add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
15×cbrt-undiv rec-exp 1-exp associate-/r/
13×associate-/r*
11×fma-neg
10×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 800
Calls
4 calls:
21.0ms
(- (- 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))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
47.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify181.0ms

Algorithm
egg-herbie
Counts
812 → 812
Iterations

Useful iterations: 1 (68.0ms)

IterNodesCost
0414111665
150019903

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.6b

regimes189.0ms

Accuracy

95.8% (1.0b remaining)

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

bsearch227.0ms

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

sample2.3s

Algorithm
intervals
Results
593.0ms5894×body80valid
522.0ms1083×body2560valid
365.0ms896×body1280valid
276.0ms2938×body80nan
141.0ms438×body640valid
67.0ms117×body5120valid
59.0ms229×body320valid
17.0ms100×body160valid