Details

Time bar (total: 5.1s)

sample36.0ms

Algorithm
intervals
Results
15.0ms280×body80valid
4.0ms86×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize79.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04183056
114712008
250011917

prune425.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize85.0ms

Local error

Found 4 expressions with local error:

10.8b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 76
Calls
4 calls:
12.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
64.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
61.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
62.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0249756
1969641
24038626
35001624

prune402.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.1b

localize85.0ms

Local error

Found 4 expressions with local error:

9.1b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

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:
17.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
63.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify178.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune420.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.1b

localize88.0ms

Local error

Found 4 expressions with local error:

9.6b
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
8×add-log-exp
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in flip3-- distribute-rgt-neg-in sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 72
Calls
4 calls:
12.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
60.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
86.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
88.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0391872
11588795
25001765

prune425.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 8.1b

regimes193.0ms

Accuracy

90.7% (1.1b remaining)

Error of 8.8b against oracle of 7.7b and baseline of 19.8b

bsearch150.0ms

Steps
ItersRangePoint
7
7.363656180201337e+60
1.0503009045500217e+63
1.0273828621120979e+63
8
-3.3847953012938245e+113
-2.3419197238566892e+109
-3.0233171392607914e+113

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04958
14958

end0.0ms

sample935.0ms

Algorithm
intervals
Results
463.0ms8770×body80valid
131.0ms2817×body80nan