Details

Time bar (total: 5.1s)

sample35.0ms

Algorithm
intervals
Results
7.0ms32×body2560valid
6.0ms182×body80valid
5.0ms28×body1280valid
4.0ms256×pre80true
1.0ms10×body640valid
0.0ms4×body320valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.1b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
27.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
29.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
278.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify72.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0280888
1816840
22500828
35001827

prune272.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ 1.0 (cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))
0.1b
(pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.3b
(cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
61×*-un-lft-identity
60×add-sqr-sqrt
59×add-cube-cbrt
54×cbrt-prod
48×unpow-prod-down cube-prod
39×sqrt-prod
10×sqrt-div
8×associate-/r/
7×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+ add-log-exp
4×div-inv
3×pow-unpow
2×cube-div cube-mult unpow3 pow-exp rem-cube-cbrt sqr-pow
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square cbrt-div pow-pow sqrt-pow1 pow1/2 pow1/3 div-exp sum-log rem-cbrt-cube distribute-lft-out
Counts
4 → 159
Calls
4 calls:
65.0ms
(+ 1.0 (cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))
20.0ms
(pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.0ms
(cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))

series330.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(+ 1.0 (cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))
116.0ms
(pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms
(cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))

simplify74.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05532175
124041918
250031820

prune349.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.3b

localize17.0ms

Local error

Found 4 expressions with local error:

9.8b
(+ 1.0 (cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.3b
(cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
52×sqrt-div
36×cbrt-prod
16×associate-/r/
15×unpow-prod-down flip3-+ cube-prod flip-+
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
8×frac-times
6×pow1 times-frac sqrt-prod add-log-exp
4×add-exp-log associate-*r/ associate-*l/ add-cbrt-cube
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
1×+-commutative cube-div cube-mult cbrt-div pow1/3 unpow3 sum-log rem-cbrt-cube distribute-lft-out sqr-pow
Counts
4 → 88
Calls
4 calls:
54.0ms
(+ 1.0 (cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)))
13.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.0ms
(cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3))

series278.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(+ 1.0 (cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
66.0ms
(cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3))

simplify60.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04451739
117411554
250021546

prune355.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.3b

localize22.0ms

Local error

Found 4 expressions with local error:

14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.3b
(cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))) 3))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
702×sqrt-div
325×cbrt-div
272×frac-times
219×flip3-+ flip-+
180×cbrt-prod
160×associate-/r/
100×associate-*r/
88×associate-*l/
87×unpow-prod-down cube-prod
15×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
9×sqrt-prod
7×pow1
6×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×div-inv
1×cube-div cube-mult pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 235
Calls
4 calls:
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
131.0ms
(cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))) 3))

series244.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(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)))
73.0ms
(cbrt (pow (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))) 3))

simplify174.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
0181512579
1481912560
2500112560

prune633.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 15.3b

regimes363.0ms

Accuracy

0% (0.9b remaining)

Error of 14.2b against oracle of 13.3b and baseline of 14.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03034
13034

end0.0ms

sample853.0ms

Algorithm
intervals
Results
212.0ms5975×body80valid
182.0ms823×body2560valid
119.0ms649×body1280valid
109.0ms8000×pre80true
48.0ms324×body640valid
16.0ms156×body320valid
5.0ms73×body160valid