Details

Time bar (total: 8.8s)

sample32.0ms

Algorithm
intervals
Results
14.0ms275×body80valid
4.0ms79×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 20.0b

Counts
2 → 1

localize111.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(+ (- b) (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)))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
659×add-sqr-sqrt
289×sqrt-prod
270×prod-diff
265×*-un-lft-identity
216×unswap-sqr
182×difference-of-squares
113×add-cube-cbrt
108×associate-*l*
89×distribute-rgt-neg-in
87×distribute-lft-neg-in
74×distribute-lft-out--
36×swap-sqr *-commutative
29×neg-mul-1
12×add-log-exp
10×fma-def fma-neg
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
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 403
Calls
4 calls:
43.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify132.0ms

Algorithm
egg-herbie
Counts
415 → 415
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
074012242
121449625
250019326

prune663.0ms

Filtered
415 candidates to 122 candidates (29.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New4087415
Fresh000
Picked101
Done000
Total4097416

Merged error: 7.3b

Counts
416 → 7

localize120.0ms

Local error

Found 4 expressions with local error:

8.4b
(- (- 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)))

rewrite611.0ms

Algorithm
rewrite-expression-head
Rules
4608×sqrt-prod
3648×add-sqr-sqrt
2716×*-un-lft-identity
1769×associate-*l*
1640×prod-diff
1173×unswap-sqr
1098×swap-sqr
982×distribute-lft-out--
906×difference-of-squares
632×add-cube-cbrt
497×distribute-rgt-neg-in
495×distribute-lft-neg-in
300×associate-*r*
200×*-commutative
165×neg-mul-1
10×fma-neg
8×add-log-exp
7×pow1
6×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×diff-log
1×associate--l- neg-sub0 sub-neg neg-log
Counts
4 → 1805
Calls
4 calls:
172.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

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)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify760.0ms

Algorithm
egg-herbie
Counts
1817 → 1817
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
01963110861
1486651013
2500151013

prune967.0ms

Filtered
1817 candidates to 149 candidates (8.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New181611817
Fresh066
Picked011
Done000
Total181681824

Merged error: 7.3b

Counts
1824 → 8

localize117.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (- b) (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)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
72×sqrt-prod
54×unswap-sqr
50×*-un-lft-identity
45×difference-of-squares
27×associate-*l*
18×distribute-lft-out--
10×add-cube-cbrt fma-def
9×swap-sqr *-commutative
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u distribute-rgt-neg-in add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 141
Calls
4 calls:
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
42.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
207.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify151.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03141304
111171273
247741261
350011261

prune567.0ms

Filtered
153 candidates to 98 candidates (64.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1530153
Fresh066
Picked011
Done011
Total1538161

Merged error: 7.3b

Counts
161 → 8

localize114.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b
(/ (* a c) b)
5.0b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
596×add-sqr-sqrt
268×times-frac
214×*-un-lft-identity
194×unswap-sqr
121×associate-*l*
119×difference-of-squares
94×add-cube-cbrt
60×associate-*r*
58×distribute-lft-out--
24×sqrt-prod associate-/l*
23×*-commutative
18×associate-/r*
14×add-exp-log add-cbrt-cube
10×fma-def
8×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u distribute-rgt-neg-in div-exp log1p-expm1-u
3×distribute-lft-neg-in swap-sqr
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 357
Calls
4 calls:
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(/ (* a c) b)
56.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(/ (* a c) b)
63.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
369 → 369
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012654499
150014392

prune1.3s

Filtered
369 candidates to 246 candidates (66.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3672369
Fresh145
Picked101
Done022
Total3698377

Merged error: 6.5b

Counts
377 → 8

regimes219.0ms

Accuracy

92.6% (1.1b remaining)

Error of 7.6b against oracle of 6.5b and baseline of 21.3b

bsearch177.0ms

Steps
ItersRangePoint
9
4.546949039871578e+116
7.0067478635952275e+121
7.587411789834341e+119
9
-1.6289578644700005e+63
-1.5322109559450533e+54
-1.6048696542769354e+63

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05962
16762
26762

end0.0ms

sample821.0ms

Algorithm
intervals
Results
434.0ms8700×body80valid
134.0ms2865×body80nan