Details

Time bar (total: 7.9s)

sample58.0ms

Algorithm
intervals
Results
13.0ms192×body80valid
11.0ms25×body2560valid
8.0ms256×pre80true
7.0ms19×body1280valid
4.0ms13×body640valid
1.0ms4×body320valid
0.0ms3×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize14.0ms

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))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite55.0ms

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:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
25.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(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 (sqrt (+ (* (* 4.0 p) p) (* x x))))
15.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify143.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune842.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.9b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
23×add-sqr-sqrt
22×add-cube-cbrt
18×times-frac
15×sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×log-pow
4×log-prod exp-prod sqrt-div
3×flip3-+ flip-+ associate-/l*
2×associate-/r/ distribute-lft-out
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp exp-sum clear-num sum-log div-inv
Counts
4 → 85
Calls
4 calls:
13.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
98.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify67.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0269900
1805835
22267823
35002822

prune1.0s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 13.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.1b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 94
Calls
4 calls:
13.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series51.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify148.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
03421278
111891191
247291163
350011145

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.1b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 94
Calls
4 calls:
13.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series54.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify148.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
03421276
111891191
247291163
350011145

prune1.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.7b

regimes691.0ms

Accuracy

0% (1.1b remaining)

Error of 14.0b against oracle of 12.9b and baseline of 14.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02920
12920

end0.0ms

sample1.5s

Algorithm
intervals
Results
429.0ms6047×body80valid
349.0ms787×body2560valid
237.0ms8000×pre80true
216.0ms581×body1280valid
91.0ms315×body640valid
35.0ms163×body320valid
15.0ms107×body160valid