Details

Time bar (total: 5.4s)

sample36.0ms

Algorithm
intervals
Results
14.0ms279×body80valid
4.0ms90×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

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:
8.0ms
(- (* b b) (* (* 4.0 a) c))
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
61.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04062988
114311956
250021869

prune382.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize87.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.1b
(/ (* a c) b)
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 87
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
33.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
9.0ms
(/ (* a c) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
155.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
21.0ms
(/ (* a c) b)
61.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0423713
12101628
25002621

prune369.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

localize92.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.0b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
30×add-exp-log *-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×associate-/r* add-log-exp unswap-sqr
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/r/ difference-of-squares
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 → 125
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
36.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
189.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
64.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify93.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07191447
136621263
250011212

prune620.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize99.0ms

Local error

Found 4 expressions with local error:

19.7b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
19.7b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
19.7b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-div
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod frac-times pow1/3 associate-*r/ associate-*l/ sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 59
Calls
4 calls:
23.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
22.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
27.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
82.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
82.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
60.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify85.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0239654
1757598
22993552
35002551

prune427.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

regimes293.0ms

Accuracy

90.7% (1.3b remaining)

Error of 8.0b against oracle of 6.7b and baseline of 20.7b

bsearch157.0ms

Steps
ItersRangePoint
6
2.905752377093217e+53
1.5130510757279288e+54
1.4394867919093142e+54
9
-3.819893964099896e+158
-6.080633474453611e+152
-7.031354366652439e+153

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06694
16694

end0.0ms

sample920.0ms

Algorithm
intervals
Results
442.0ms8711×body80valid
137.0ms2998×body80nan