Details

Time bar (total: 5.7s)

sample52.0ms

Algorithm
intervals
Results
28.0ms281×body80valid
8.0ms87×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize118.0ms

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)))

rewrite13.0ms

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 flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
2.0ms
(- (* 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)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0149478
1576446
22486444
35001440

prune252.0ms

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)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
6.0ms
(- (- 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)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- 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)))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify105.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0225725
1835631
23414609
35001589

prune324.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.9b

localize118.0ms

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)))

rewrite55.0ms

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 div-exp 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 diff-log flip-+
Counts
4 → 75
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
178.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
18.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0392629
11966544
25001541

prune315.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.2b

localize126.0ms

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)))

rewrite268.0ms

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×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 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 113
Calls
4 calls:
2.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
235.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
47.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
351.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06871327
135201144
250011102

prune503.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.2b

regimes215.0ms

Accuracy

88.5% (1.4b remaining)

Error of 8.4b against oracle of 7.0b and baseline of 19.4b

bsearch132.0ms

Steps
ItersRangePoint
7
6.184155830638016e+27
1.3306260697673677e+30
1.2919983862558445e+30
4
-3.05654141344836e+116
-2.129980745276144e+116
-3.0275863925679783e+116

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06266
16266

end0.0ms

sample1.4s

Algorithm
intervals
Results
884.0ms8744×body80valid
275.0ms2910×body80nan