Details

Time bar (total: 4.2s)

sample40.0ms

Algorithm
intervals
Results
7.0ms184×body80valid
6.0ms28×body2560valid
6.0ms31×body1280valid
3.0ms91×body80nan
3.0ms20×body640valid
1.0ms5×body5120valid
0.0ms6×body160valid
0.0ms3×body320valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

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: 33.3b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
8×add-cube-cbrt add-log-exp
7×times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
4×prod-exp cbrt-unprod
3×flip3-- distribute-rgt-neg-in associate-*l* pow-prod-down flip--
2×cbrt-undiv sqrt-div diff-log div-exp associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative div-inv
Counts
4 → 83
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
14.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series259.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* 4.0 (* a c))
93.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0451853
11636764
25001759

prune235.0ms

Filtered
95 candidates to 66 candidates (69.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New88795
Fresh000
Picked101
Done000
Total89796

Merged error: 5.6b

Counts
96 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
58×add-sqr-sqrt
57×*-un-lft-identity
30×add-exp-log
29×add-cube-cbrt
20×associate-/r*
18×add-cbrt-cube
14×div-exp distribute-lft-out-- difference-of-squares
11×associate-/r/
10×sqrt-prod
8×add-log-exp
7×cbrt-undiv flip3-- distribute-rgt-neg-in flip--
6×pow1 div-inv
4×prod-exp associate-/l*
3×rec-exp 1-exp
2×frac-2neg sqrt-div diff-log clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 neg-log inv-pow
Counts
4 → 144
Calls
4 calls:
11.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series435.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
111.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05682115
127441859
250011788

prune288.0ms

Filtered
156 candidates to 85 candidates (54.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1524156
Fresh336
Picked101
Done000
Total1567163

Merged error: 5.5b

Counts
163 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.3b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×add-sqr-sqrt
18×add-cbrt-cube
17×*-un-lft-identity
13×prod-exp
12×pow1
10×associate-*l*
9×add-cube-cbrt
8×associate-*r* add-log-exp
7×cbrt-unprod
5×sqrt-prod
4×flip3-- div-exp pow-prod-down flip-- distribute-lft-out-- difference-of-squares
3×times-frac
2×cbrt-undiv frac-times rec-exp distribute-rgt-neg-in sqrt-div diff-log 1-exp associate-*l/ *-commutative
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log un-div-inv div-inv unswap-sqr
Counts
4 → 91
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
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
(sqrt (- (* b b) (* 4.0 (* a c))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* 4.0 (* a c))
93.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
94.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0516954
12203829
25001820

prune224.0ms

Filtered
103 candidates to 66 candidates (64.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1021103
Fresh156
Picked011
Done000
Total1037110

Merged error: 5.5b

Counts
110 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
8×add-cube-cbrt add-log-exp
7×times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
4×prod-exp cbrt-unprod
3×flip3-- distribute-rgt-neg-in associate-*l* pow-prod-down flip--
2×cbrt-undiv sqrt-div diff-log div-exp associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative div-inv
Counts
4 → 83
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
12.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series259.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* 4.0 (* a c))
91.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0451853
11636764
25001759

prune216.0ms

Filtered
95 candidates to 66 candidates (69.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New94195
Fresh145
Picked011
Done011
Total957102

Merged error: 5.5b

Counts
102 → 7

regimes235.0ms

Accuracy

86.1% (3.9b remaining)

Error of 9.6b against oracle of 5.7b and baseline of 34.0b

bsearch184.0ms

Steps
ItersRangePoint
7
6.66182219120084e+105
6.051047097450507e+107
4.075293091096083e+107
4
-4.559231648305547e-75
-2.6944994336787596e-75
-4.322102267327746e-75
8
-0.42001306818412604
-0.00020221124262352014
-0.0002601540763239523
7
-2.7078859601421552e+87
-1.2247309707199115e+86
-6.22368915403742e+86

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05537
15537

end0.0ms

sample1.1s

Algorithm
intervals
Results
253.0ms1096×body2560valid
222.0ms5817×body80valid
174.0ms941×body1280valid
108.0ms2942×body80nan
63.0ms434×body640valid
35.0ms129×body5120valid
29.0ms236×body320valid
7.0ms92×body160valid