Details

Time bar (total: 9.7s)

sample3.5s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 38.916016%

Results
12.0ms256×body80valid
0.0ms9×body80invalid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.6b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
1.1b
(+ (* a c) (* b d))
28.0b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×pow1 associate-/r* associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 53
Calls
3 calls:
4.0ms
(+ (* c c) (* d d))
8.0ms
(+ (* a c) (* b d))
9.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series41.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* c c) (* d d))
9.0ms
(+ (* a c) (* b d))
26.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify135.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0272527
11164479
24437477
35002477

prune124.0ms

Filtered
49 candidates to 62 candidates (-26.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New53962
Fresh000
Picked101
Done000
Total54963

Merged error: 27.8b

Counts
63 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (* a c) (* b d))
17.9b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.0b
(sqrt (+ (* c c) (* d d)))
30.0b
(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
3.0ms
(+ (* a c) (* b d))
10.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
3.0ms
(sqrt (+ (* c c) (* d d)))

series57.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (* a c) (* b d))
34.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
8.0ms
(sqrt (+ (* c c) (* d d)))

simplify84.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0273893
1868840
22679828
35002828

prune144.0ms

Filtered
74 candidates to 96 candidates (-29.7%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New91596
Fresh268
Picked011
Done000
Total9312105

Merged error: 24.8b

Counts
105 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (* a c) (* b d))
17.9b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.0b
(sqrt (+ (* c c) (* d d)))
30.0b
(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
3.0ms
(+ (* a c) (* b d))
9.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series55.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (* a c) (* b d))
34.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

simplify85.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0273893
1868840
22679828
35002828

prune142.0ms

Filtered
74 candidates to 96 candidates (-29.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New95196
Fresh1910
Picked011
Done011
Total9612108

Merged error: 24.8b

Counts
108 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
1.1b
(+ (* a c) (* b d))
27.6b
(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
8×flip3-+ div-exp flip-+ add-log-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv
2×+-commutative rec-exp frac-2neg 1-exp clear-num sum-log associate-/l/
1×pow-flip inv-pow
Counts
4 → 137
Calls
4 calls:
3.0ms
(+ (* c c) (* d d))
9.0ms
(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
3.0ms
(+ (* a c) (* b d))
9.0ms
(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (* c c) (* d d))
28.0ms
(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
10.0ms
(+ (* a c) (* b d))
18.0ms
(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify71.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05181819
126321654
250011567

prune106.0ms

Filtered
84 candidates to 149 candidates (-77.4%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1481149
Fresh279
Picked011
Done022
Total15011161

Merged error: 24.8b

Counts
161 → 11

regimes394.0ms

Accuracy

6% (2.8b remaining)

Error of 26.8b against oracle of 24.0b and baseline of 27.0b

bsearch22.0ms

Steps
ItersRangePoint
7
9.689596692723121e+104
1.618325976083375e+106
1.5745261133001897e+106

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02619
12619

end0.0ms

sample4.5s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 38.916016%

Results
410.0ms8000×body80valid
22.0ms447×body80invalid

Profiling

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