Details

Time bar (total: 3.5s)

sample43.0ms

Algorithm
intervals
Results
11.0ms199×body80valid
5.0ms17×body2560valid
5.0ms19×body1280valid
5.0ms256×pre80true
2.0ms10×body640valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.9b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
5.0ms
(+ (* (* 4.0 p) p) (* x x))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series36.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
9.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify155.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0278822
11014772
24232757
35001757

prune198.0ms

Filtered
67 candidates to 91 candidates (-35.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New811091
Fresh000
Picked011
Done000
Total811192

Merged error: 12.6b

Counts
92 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.2b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
14×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp
7×pow1
5×unswap-sqr
4×flip3-+ sqrt-div prod-exp flip-+
3×associate-*l*
2×+-commutative div-exp sum-log associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
5.0ms
(+ (* (* 4.0 p) p) (* x x))
15.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series38.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
9.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify53.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0387817
11913734
25002700

prune191.0ms

Filtered
68 candidates to 98 candidates (-44.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New94498
Fresh369
Picked101
Done101
Total9910109

Merged error: 12.6b

Counts
109 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) 1)) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
6.8b
(+ 1.0 (* (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) 1)) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
18.9b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
18.9b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
66×add-exp-log
38×add-sqr-sqrt
33×times-frac associate-*r*
32×prod-exp
27×add-cube-cbrt *-un-lft-identity
25×add-cbrt-cube
22×div-exp
20×sqrt-prod
16×cbrt-prod
12×1-exp
8×cbrt-unprod
7×cbrt-undiv associate-*l*
6×pow1 rec-exp cbrt-div add-log-exp
4×flip3-+ flip-+ unswap-sqr
2×pow1/3 sqrt-div associate-/r/ div-inv
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 119
Calls
4 calls:
20.0ms
(* (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) 1)) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
3.0ms
(+ 1.0 (* (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) 1)) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series177.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) 1)) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
69.0ms
(+ 1.0 (* (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) 1)) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
25.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify85.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07962273
133881983
250011966

prune393.0ms

Filtered
91 candidates to 131 candidates (-44.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1265131
Fresh459
Picked101
Done000
Total13110141

Merged error: 12.6b

Counts
141 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

7.8b
(+ 1.0 (* (/ 1 (* (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))) (/ x (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.9b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod add-log-exp
4×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
3×cbrt-prod
2×rem-sqrt-square cbrt-div sqrt-pow1 pow1/2
1×+-commutative pow1/3 sum-log
Counts
4 → 54
Calls
4 calls:
3.0ms
(+ 1.0 (* (/ 1 (* (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))) (/ x (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series110.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(+ 1.0 (* (/ 1 (* (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))) (/ x (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0339917
11162847
25002844

prune273.0ms

Filtered
60 candidates to 66 candidates (-10.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New64266
Fresh279
Picked101
Done000
Total67976

Merged error: 12.6b

Counts
76 → 9

regimes217.0ms

Accuracy

0% (1.7b remaining)

Error of 14.9b against oracle of 13.2b and baseline of 14.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03429
13429

end0.0ms

sample1.3s

Algorithm
intervals
Results
327.0ms6008×body80valid
250.0ms767×body2560valid
166.0ms628×body1280valid
148.0ms8000×pre80true
69.0ms334×body640valid
28.0ms171×body320valid
10.0ms92×body160valid

Profiling

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