Details

Time bar (total: 9.8s)

sample40.0ms

Algorithm
intervals
Results
7.0ms34×body2560valid
6.0ms172×body80valid
5.0ms32×body1280valid
3.0ms79×body80nan
2.0ms9×body5120valid
2.0ms16×body640valid
1.0ms9×body320valid
0.0ms3×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

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: 35.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b
(- (* b b) (* (* 3.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
330×associate-*l* prod-diff
309×*-un-lft-identity
229×add-cube-cbrt
177×associate-*r*
125×unswap-sqr
75×swap-sqr
65×*-commutative
60×times-frac
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
17×distribute-rgt-neg-in
15×fma-neg
12×associate-/r* distribute-lft-out--
10×fma-def add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 541
Calls
4 calls:
44.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
33.0ms
(- (* b b) (* (* 3.0 a) c))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
44.0ms
(- (* b b) (* (* 3.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify104.0ms

Algorithm
egg-herbie
Counts
553 → 553
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
014219182
150016679

prune694.0ms

Filtered
553 candidates to 170 candidates (30.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New54310553
Fresh000
Picked101
Done000
Total54410554

Merged error: 6.1b

Counts
554 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
451×add-sqr-sqrt
330×prod-diff
327×associate-*l*
230×*-un-lft-identity
202×add-cube-cbrt
165×associate-*r*
123×unswap-sqr
75×swap-sqr
61×*-commutative
30×difference-of-squares
24×sqrt-prod
15×fma-neg
12×distribute-lft-out--
10×pow1 fma-def add-log-exp
9×add-exp-log add-cbrt-cube
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in pow-prod-down prod-exp cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log neg-log flip-+
Counts
4 → 478
Calls
4 calls:
8.0ms
(* (* 3.0 a) c)
30.0ms
(- (* b b) (* (* 3.0 a) c))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
44.0ms
(- (* b b) (* (* 3.0 a) c))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify167.0ms

Algorithm
egg-herbie
Counts
490 → 490
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
011817838
137965390
250015385

prune525.0ms

Filtered
490 candidates to 135 candidates (27.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4873490
Fresh369
Picked101
Done000
Total4919500

Merged error: 6.1b

Counts
500 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt 3.0) a)
0.8b
(- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c)))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c)))))
23.2b
(sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c))))

rewrite949.0ms

Algorithm
rewrite-expression-head
Rules
4933×add-sqr-sqrt
2762×unswap-sqr
1425×prod-diff
1144×cbrt-prod
1139×associate-*l*
876×associate-*r*
767×*-un-lft-identity
731×add-cube-cbrt
656×swap-sqr
370×difference-of-squares
331×*-commutative
195×sqrt-prod
15×fma-neg
14×distribute-lft-out--
10×fma-def add-log-exp
7×pow1 add-cbrt-cube
6×add-exp-log
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in
2×flip3-- sqrt-div sum-log flip-- cbrt-unprod distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log pow-prod-down neg-log prod-exp flip-+
Counts
4 → 1907
Calls
4 calls:
5.0ms
(* (cbrt 3.0) a)
115.0ms
(- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c)))
159.0ms
(+ (- b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c)))))
184.0ms
(sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cbrt 3.0) a)
91.0ms
(- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c)))
137.0ms
(+ (- b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c)))))
130.0ms
(sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* (* (cbrt 3.0) a) c))))

simplify630.0ms

Algorithm
egg-herbie
Counts
1919 → 1919
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0404679471
1500275417

prune2.6s

Filtered
1919 candidates to 515 candidates (26.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New191901919
Fresh088
Picked011
Done000
Total191991928

Merged error: 6.1b

Counts
1928 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt 3.0) a)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
447×add-sqr-sqrt
330×prod-diff
318×associate-*l*
229×*-un-lft-identity
201×add-cube-cbrt
162×associate-*r*
121×unswap-sqr
75×swap-sqr
60×*-commutative
30×difference-of-squares
24×sqrt-prod
15×fma-neg
12×distribute-lft-out--
10×fma-def add-log-exp
7×pow1 add-cbrt-cube
6×add-exp-log
4×cbrt-prod expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in
2×flip3-- sqrt-div sum-log flip-- cbrt-unprod distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log pow-prod-down neg-log prod-exp flip-+
Counts
4 → 470
Calls
4 calls:
4.0ms
(* (cbrt 3.0) a)
30.0ms
(- (* b b) (* (* 3.0 a) c))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cbrt 3.0) a)
47.0ms
(- (* b b) (* (* 3.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify162.0ms

Algorithm
egg-herbie
Counts
482 → 482
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
011887820
137575371
250015366

prune575.0ms

Filtered
482 candidates to 131 candidates (27.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4820482
Fresh077
Picked011
Done011
Total4829491

Merged error: 6.1b

Counts
491 → 9

regimes382.0ms

Accuracy

84.9% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 33.9b

bsearch83.0ms

Steps
ItersRangePoint
4
2.7062129888597453e-95
4.861630376334293e-95
3.8681552371770574e-95
9
-1.8864815038392082e+94
-1.5243980513895428e+89
-9.911609721462535e+93

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03821
13821

end0.0ms

sample1.1s

Algorithm
intervals
Results
234.0ms1054×body2560valid
214.0ms5816×body80valid
153.0ms889×body1280valid
102.0ms2865×body80nan
63.0ms470×body640valid
29.0ms111×body5120valid
24.0ms235×body320valid
8.0ms125×body160valid