Details

Time bar (total: 5.7s)

sample35.0ms

Algorithm
intervals
Results
15.0ms278×body80valid
5.0ms101×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize118.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04062988
114311956
250021869

prune393.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize120.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
3.6b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.9b
(/ (* a c) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 81
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
3.0ms
(/ (* a c) b)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
19.0ms
(/ (* a c) b)
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0423633
12069555
25001550

prune362.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.5b

localize128.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
3.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.6b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×times-frac
30×add-exp-log
23×add-cbrt-cube
22×add-cube-cbrt *-un-lft-identity associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×add-log-exp unswap-sqr
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-/r* sqrt-prod flip-- div-inv
2×sqrt-div associate-/r/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 119
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
84.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
51.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
98.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify92.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07161341
136501165
250011114

prune560.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.5b

localize132.0ms

Local error

Found 4 expressions with local error:

4.1b
(cbrt (/ c (cbrt b)))
4.1b
(cbrt (/ c (cbrt b)))
4.1b
(cbrt (/ c (cbrt b)))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
93×cbrt-prod
54×times-frac
45×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 116
Calls
4 calls:
2.0ms
(cbrt (/ c (cbrt b)))
2.0ms
(cbrt (/ c (cbrt b)))
2.0ms
(cbrt (/ c (cbrt b)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series567.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(cbrt (/ c (cbrt b)))
167.0ms
(cbrt (/ c (cbrt b)))
163.0ms
(cbrt (/ c (cbrt b)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0281978
1865952
23747944
35001923

prune742.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.5b

regimes200.0ms

Accuracy

91.9% (1.1b remaining)

Error of 8.0b against oracle of 6.9b and baseline of 20.0b

bsearch194.0ms

Steps
ItersRangePoint
7
7.8930669794294e+68
1.794276654474529e+70
1.7701741483501238e+70
9
-4.2740907516194833e+155
-3.627510837665024e+149
-1.3386170315757073e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08491
18491

end0.0ms

sample844.0ms

Algorithm
intervals
Results
463.0ms8734×body80valid
138.0ms2874×body80nan