Details

Time bar (total: 5.2s)

sample34.0ms

Algorithm
intervals
Results
15.0ms277×body80valid
4.0ms82×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: 18.6b

localize117.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(+ (- 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)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(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

prune454.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.9b

localize114.0ms

Local error

Found 4 expressions with local error:

13.0b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

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:
11.0ms
(+ (- 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)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (- 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)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (111.0ms)

IterNodesCost
0249756
1969641
24038626
35001624

prune416.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.9b

localize135.0ms

Local error

Found 4 expressions with local error:

6.7b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.9b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.9b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×sqrt-prod
2×neg-mul-1 pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 83
Calls
4 calls:
13.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify59.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04281492
116671341
250021297

prune467.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.9b

localize120.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.8b
(/ (* a c) b)
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
54×*-un-lft-identity
50×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×times-frac
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u associate-/l*
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub neg-log
Counts
4 → 156
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
3.0ms
(/ (* a c) b)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
19.0ms
(/ (* a c) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify88.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06513102
127072019
250021941

prune431.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.6b

regimes227.0ms

Accuracy

86.4% (1.8b remaining)

Error of 8.3b against oracle of 6.5b and baseline of 19.9b

bsearch105.0ms

Steps
ItersRangePoint
0
3459389182982077.0
3464539799267021.5
3461964491124549.0
9
-1.2845883854340997e+78
-5.15156631625478e+72
-1.0088663643419234e+78

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05863
15863

end0.0ms

sample861.0ms

Algorithm
intervals
Results
459.0ms8729×body80valid
152.0ms2961×body80nan