Details

Time bar (total: 4.7s)

sample33.0ms

Algorithm
intervals
Results
7.0ms202×body80valid
5.0ms23×body2560valid
4.0ms256×pre80true
3.0ms15×body1280valid
2.0ms11×body640valid
0.0ms4×body320valid
0.0ms1×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize12.0ms

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))))
0.2b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×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×expm1-log1p-u fma-def flip3-+ sqrt-div flip-+ log1p-expm1-u
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 → 91
Calls
4 calls:
5.0ms
(+ (* (* 4.0 p) p) (* x x))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* (* 4.0 p) p) (* x x))
57.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify158.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (148.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune319.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.5b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
21×*-un-lft-identity
19×add-cube-cbrt
18×pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times log1p-expm1-u
3×fma-def
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 136
Calls
4 calls:
21.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (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)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03051424
111511313
250011274

prune414.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

localize19.0ms

Local error

Found 4 expressions with local error:

7.0b
(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
6×sqrt-div add-log-exp
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
3×rem-sqrt-square fma-def sqrt-pow1 pow1/2
1×+-commutative sum-log distribute-lft-out
Counts
4 → 68
Calls
4 calls:
11.0ms
(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* 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
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify110.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0270956
1927891
24255890
35001890

prune418.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

localize26.0ms

Local error

Found 4 expressions with local error:

7.0b
(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
6×sqrt-div add-log-exp
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
3×rem-sqrt-square fma-def sqrt-pow1 pow1/2
1×+-commutative sum-log distribute-lft-out
Counts
4 → 68
Calls
4 calls:
10.0ms
(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* 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
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(+ 1.0 (/ x (* (* (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify110.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0270956
1927891
24255890
35001890

prune461.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.8b

regimes369.0ms

Accuracy

0% (0.2b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0199
1199

end0.0ms

sample850.0ms

Algorithm
intervals
Results
215.0ms6007×body80valid
189.0ms824×body2560valid
113.0ms628×body1280valid
110.0ms8000×pre80true
44.0ms316×body640valid
16.0ms154×body320valid
5.0ms71×body160valid