Details

Time bar (total: 6.0s)

sample42.0ms

Algorithm
intervals
Results
8.0ms38×body2560valid
7.0ms177×body80valid
5.0ms26×body1280valid
4.0ms112×body80nan
3.0ms20×body640valid
2.0ms6×body5120valid
1.0ms9×body320valid
0.0ms4×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: 34.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.6b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

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:
38.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* 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))))

series308.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0403779
11514685
25002674

prune221.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.8b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series484.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
186.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06402692
129442439
250012426

prune427.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize14.0ms

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)))))))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.1b
(/ (* 2.0 a) (* 4.0 (* a c)))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite95.0ms

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
12×add-sqr-sqrt
11×*-un-lft-identity
8×pow1 rec-exp 1-exp add-log-exp
7×add-cube-cbrt
5×associate-/r/
4×flip3-- times-frac sqrt-prod flip-- associate-/l*
2×frac-times pow-flip frac-2neg sqrt-div diff-log associate-*r/ clear-num associate-/r* div-inv distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ inv-pow
Counts
4 → 115
Calls
4 calls:
66.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
07301524
140741199
250011177

prune250.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite121.0ms

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:
31.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series218.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
45.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify152.0ms

Algorithm
egg-herbie
Counts
732 → 732
Iterations

Useful iterations: 1 (64.0ms)

IterNodesCost
039579260
150018107

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.6b

regimes142.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 30.4b

bsearch177.0ms

Steps
ItersRangePoint
9
2.6683347110001497e+63
3.895668027475672e+69
6.6664567809045535e+68
6
-8.36501767772797e-260
-8.1135434350231975e-261
-2.3757722518657493e-260
9
-1.2294333374423815e+100
-1.4471431684397531e+91
-4.301018409236461e+98

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04525
14525

end0.0ms

sample1.1s

Algorithm
intervals
Results
245.0ms1085×body2560valid
230.0ms5822×body80valid
164.0ms888×body1280valid
105.0ms2903×body80nan
64.0ms453×body640valid
27.0ms99×body5120valid
26.0ms244×body320valid
14.0ms123×body160valid