Details

Time bar (total: 4.1s)

sample54.0ms

Algorithm
intervals
Results
11.0ms39×body2560valid
9.0ms180×body80valid
5.0ms26×body640valid
5.0ms20×body1280valid
4.0ms91×body80nan
3.0ms5×body160valid
1.0ms9×body320valid
1.0ms3×body5120valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune5.0ms

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: 35.0b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
16.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05903305
121012212
250022128

prune296.0ms

Filtered
169 candidates to 89 candidates (52.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1618169
Fresh000
Picked101
Done000
Total1628170

Merged error: 3.3b

Counts
170 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07184221
130992976
250012863

prune288.0ms

Filtered
217 candidates to 97 candidates (44.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2152217
Fresh167
Picked011
Done000
Total2169225

Merged error: 3.2b

Counts
225 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
15.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
71.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify83.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06563422
125942238
250012193

prune268.0ms

Filtered
177 candidates to 89 candidates (50.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1761177
Fresh167
Picked011
Done011
Total1779186

Merged error: 3.2b

Counts
186 → 9

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New000
Fresh066
Picked011
Done022
Total099

Merged error: 3.2b

Counts
9 → 9

regimes194.0ms

Accuracy

83.6% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.7b

bsearch249.0ms

Steps
ItersRangePoint
10
1.5450168366677492e+128
2.0521185469434633e+142
3.9701546350182474e+129
11
-1.0303076794227059e-155
-1.0133968715090831e-176
-9.097853122909879e-156
5
-1.4643227903530048e-124
-6.030931541348017e-125
-6.313023766163172e-125
9
-2.2447030685571666e-91
-2.829998530983053e-96
-1.3786658632014202e-92

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04934
14934

end0.0ms

sample1.4s

Algorithm
intervals
Results
312.0ms1062×body2560valid
303.0ms5805×body80valid
217.0ms918×body1280valid
149.0ms2977×body80nan
87.0ms464×body640valid
46.0ms123×body5120valid
38.0ms240×body320valid
12.0ms120×body160valid