Details

Time bar (total: 5.3s)

sample33.0ms

Algorithm
intervals
Results
14.0ms278×body80valid
3.0ms71×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize118.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

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:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (- b) (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)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04183056
114712008
250011917

prune440.0ms

Filtered
163 candidates to 92 candidates (56.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.6b

localize119.0ms

Local error

Found 4 expressions with local error:

6.9b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

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:
8.0ms
(- (- 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))))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
95.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04281492
116671341
250021297

prune493.0ms

Filtered
95 candidates to 79 candidates (83.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.6b

localize120.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 66
Calls
4 calls:
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)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0215611
1688585
22689580
35001577

prune462.0ms

Filtered
78 candidates to 68 candidates (87.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.6b

localize125.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.6b
(/ (* a c) b)
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt
10×fma-def
9×times-frac associate-/r*
8×add-log-exp
6×distribute-rgt-neg-in
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out--
3×distribute-lft-neg-in sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l* difference-of-squares
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 98
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
188.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
20.0ms
(/ (* a c) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0476777
12207680
25001672

prune404.0ms

Filtered
110 candidates to 84 candidates (76.4%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.4b

regimes170.0ms

Accuracy

85.5% (1.9b remaining)

Error of 8.5b against oracle of 6.6b and baseline of 19.8b

bsearch181.0ms

Steps
ItersRangePoint
6
4.659640959833754e+64
2.871891476161473e+65
1.7848646122762274e+65
10
-1.7519803517262024e+185
-4.678818969655266e+173
-4.7251895122821543e+173

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06164
16164

end0.0ms

sample858.0ms

Algorithm
intervals
Results
457.0ms8702×body80valid
142.0ms2950×body80nan