Details

Time bar (total: 3.6s)

sample53.0ms

Algorithm
intervals
Results
11.0ms214×body80valid
8.0ms28×body2560valid
5.0ms19×body1280valid
4.0ms87×body80nan
2.0ms10×body640valid
1.0ms2×body5120valid
1.0ms4×body320valid
0.0ms2×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

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: 32.9b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series66.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0396773
11550683
25001673

prune161.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New74882
Fresh000
Picked011
Done000
Total74983

Merged error: 7.5b

Counts
83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.7b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series76.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05281585
125961372
250011305

prune162.0ms

Filtered
126 candidates to 72 candidates (42.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1224126
Fresh347
Picked101
Done011
Total1269135

Merged error: 7.4b

Counts
135 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.7b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
333×times-frac
221×*-un-lft-identity
122×add-sqr-sqrt
121×add-cube-cbrt
87×add-exp-log
58×div-exp
50×distribute-lft-out
31×div-inv
25×distribute-rgt-neg-in add-cbrt-cube
21×associate-/r*
17×associate-/r/
15×rec-exp 1-exp
13×cbrt-undiv
12×prod-exp
10×add-log-exp
9×flip3-+ flip-+
7×associate-/l*
5×pow1
3×sqrt-prod
2×flip3-- sqrt-div sum-log flip-- cbrt-unprod
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num associate-/l/
Counts
4 → 263
Calls
4 calls:
18.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011144690
150014131

prune337.0ms

Filtered
275 candidates to 118 candidates (57.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2750275
Fresh077
Picked011
Done011
Total2759284

Merged error: 7.4b

Counts
284 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
9.3b
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log
1×+-commutative neg-sub0 associate-+l- sub-neg flip3-+ diff-log neg-log flip-+
Counts
4 → 55
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series56.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify141.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
0246648
11010537
24598525
35001523

prune139.0ms

Filtered
67 candidates to 54 candidates (19.4%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New67067
Fresh066
Picked011
Done022
Total67976

Merged error: 7.4b

Counts
76 → 9

regimes419.0ms

Accuracy

86.5% (3.6b remaining)

Error of 9.6b against oracle of 6.0b and baseline of 32.5b

bsearch65.0ms

Steps
ItersRangePoint
8
3.2772367798370246e-46
8.826811452738637e-44
5.513140388042354e-45
8
-7.483396380019031e+117
-3.515939334884751e+113
-1.0192218364023762e+116

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03315
13315

end0.0ms

sample1.4s

Algorithm
intervals
Results
356.0ms6480×body80valid
255.0ms824×body2560valid
167.0ms662×body1280valid
135.0ms2649×body80nan
72.0ms358×body640valid
35.0ms95×body5120valid
24.0ms162×body320valid
9.0ms89×body160valid

Profiling

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