Details

Time bar (total: 9.4s)

sample41.0ms

Algorithm
intervals
Results
19.0ms281×body80valid
5.0ms113×body80nan

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 21.6b

Counts
2 → 1

localize120.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite200.0ms

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:
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
39.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify143.0ms

Algorithm
egg-herbie
Counts
415 → 415
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
073312242
120679625
250019326

prune574.0ms

Filtered
415 candidates to 122 candidates (70.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4078415
Fresh000
Picked101
Done000
Total4088416

Merged error: 7.1b

Counts
416 → 8

localize121.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
1042×add-sqr-sqrt
600×prod-diff
460×*-un-lft-identity
411×associate-*l*
317×unswap-sqr
300×add-cube-cbrt
289×sqrt-prod
197×difference-of-squares
159×associate-*r*
108×swap-sqr
92×*-commutative
85×distribute-rgt-neg-in
84×distribute-lft-neg-in
80×distribute-lft-out--
28×neg-mul-1
25×fma-neg
10×add-log-exp
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 756
Calls
4 calls:
32.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify261.0ms

Algorithm
egg-herbie
Counts
768 → 768
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
0150319210
1423213924
2500113919

prune989.0ms

Filtered
768 candidates to 158 candidates (79.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New7662768
Fresh257
Picked101
Done000
Total7697776

Merged error: 7.1b

Counts
776 → 7

localize125.0ms

Local error

Found 4 expressions with local error:

14.3b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite608.0ms

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:
164.0ms
(- (- 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)))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
41.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify778.0ms

Algorithm
egg-herbie
Counts
1817 → 1817
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
01953110861
1477751013
2500151003

prune923.0ms

Filtered
1817 candidates to 150 candidates (91.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New181521817
Fresh066
Picked101
Done000
Total181681824

Merged error: 7.1b

Counts
1824 → 8

localize139.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(+ (- (* (cbrt a) c)) (* (cbrt a) c))
22.9b
(sqrt (+ (fma b b (- (* (* (cbrt a) c) (* 4.0 (* (cbrt a) (cbrt a)))))) (* (* 4.0 (* (cbrt a) (cbrt a))) (+ (- (* (cbrt a) c)) (* (cbrt a) c)))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
705×add-sqr-sqrt
305×*-un-lft-identity
271×sqrt-prod
270×prod-diff
233×unswap-sqr
167×difference-of-squares
157×associate-*l*
139×add-cube-cbrt
129×distribute-lft-neg-in
119×distribute-rgt-neg-in
68×distribute-lft-out--
40×*-commutative
38×cbrt-prod
36×fma-def
35×swap-sqr
33×neg-mul-1
29×distribute-rgt-out
23×distribute-lft-out
20×associate-*r*
12×add-log-exp
11×hypot-def
10×fma-neg
6×pow1
4×add-exp-log expm1-log1p-u distribute-lft1-in sqrt-div add-cbrt-cube log1p-expm1-u
2×neg-sub0 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log neg-log sum-log flip-- flip-+
1×+-commutative associate--l- associate-+l- sub-neg
Counts
4 → 473
Calls
4 calls:
39.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms
(+ (- (* (cbrt a) c)) (* (cbrt a) c))
93.0ms
(sqrt (+ (fma b b (- (* (* (cbrt a) c) (* 4.0 (* (cbrt a) (cbrt a)))))) (* (* 4.0 (* (cbrt a) (cbrt a))) (+ (- (* (cbrt a) c)) (* (cbrt a) c)))))
41.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0ms
(+ (- (* (cbrt a) c)) (* (cbrt a) c))
107.0ms
(sqrt (+ (fma b b (- (* (* (cbrt a) c) (* 4.0 (* (cbrt a) (cbrt a)))))) (* (* 4.0 (* (cbrt a) (cbrt a))) (+ (- (* (cbrt a) c)) (* (cbrt a) c)))))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify210.0ms

Algorithm
egg-herbie
Counts
485 → 485
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
099612660
133569883
250019781

prune1.3s

Filtered
485 candidates to 181 candidates (62.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4850485
Fresh077
Picked011
Done000
Total4858493

Merged error: 7.1b

Counts
493 → 8

regimes246.0ms

Accuracy

90.4% (1.2b remaining)

Error of 8.8b against oracle of 7.7b and baseline of 19.7b

bsearch101.0ms

Steps
ItersRangePoint
0
1.3836563058951246e+50
1.390978468581987e+50
1.3873173872385558e+50
8
-8.122802074996069e+81
-2.6359676868927157e+78
-7.950168319619967e+81

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07471
18471
28671
38671

end0.0ms

sample848.0ms

Algorithm
intervals
Results
462.0ms8767×body80valid
141.0ms2796×body80nan