Details

Time bar (total: 5.9s)

sample50.0ms

Algorithm
intervals
Results
27.0ms281×body80valid
8.0ms87×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize115.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0170540
1665506
22968498
35001488

prune302.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.9b

localize119.0ms

Local error

Found 4 expressions with local error:

8.5b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
8.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify182.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune426.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.9b

localize121.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
5.2b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.6b
(/ (* a c) b)
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt
8×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×sqrt-prod
2×flip3-- distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 85
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
40.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
3.0ms
(/ (* a c) b)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
182.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
19.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0418685
12079598
25001591

prune361.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.2b

localize127.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
3.8b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
5.2b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite277.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
33×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×add-log-exp unswap-sqr
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out
3×sqrt-prod div-inv
2×flip3-- distribute-rgt-neg-in sqrt-div associate-/r/ flip--
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 123
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
241.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
53.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
215.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify85.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07141403
136361218
250031165

prune562.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.2b

regimes202.0ms

Accuracy

88.2% (1.5b remaining)

Error of 8.5b against oracle of 7.0b and baseline of 19.4b

bsearch135.0ms

Steps
ItersRangePoint
7
6.184155830638016e+27
1.3306260697673677e+30
1.2919983862558445e+30
4
-3.05654141344836e+116
-2.129980745276144e+116
-2.9117663090464514e+116

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06178
16178

end0.0ms

sample1.3s

Algorithm
intervals
Results
826.0ms8744×body80valid
263.0ms2910×body80nan