Details

Time bar (total: 4.4s)

sample33.0ms

Algorithm
intervals
Results
6.0ms186×body80valid
5.0ms25×body2560valid
3.0ms19×body1280valid
3.0ms256×pre80true
3.0ms21×body640valid
0.0ms2×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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite133.0ms

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:
30.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
19.0ms
(+ (* (* 4.0 p) p) (* x x))
54.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
27.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
33.0ms
(+ (* (* 4.0 p) p) (* x x))
75.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify149.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune261.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.7b
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
13.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×times-frac
25×*-un-lft-identity
23×add-cube-cbrt
12×unpow-prod-down
9×add-exp-log
8×associate-/l*
7×sqrt-prod
6×pow1 add-cbrt-cube add-log-exp
4×sqrt-div unpow2 sqr-pow
3×flip3-+ div-exp associate-/r* flip-+ difference-of-squares
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log pow-exp clear-num flip-- div-inv distribute-lft-out--
Counts
4 → 97
Calls
4 calls:
55.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
32.0ms
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
26.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
52.0ms
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03251030
11289956
25001954

prune471.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

localize12.0ms

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)))))
3.3b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite129.0ms

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:
17.0ms
(+ (* (* 4.0 p) p) (* x x))
76.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
27.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (* (* 4.0 p) p) (* x x))
53.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0387817
11913734
25002700

prune285.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
6.9b
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
9×times-frac
6×add-exp-log cbrt-prod add-cbrt-cube add-log-exp
4×pow1 cbrt-div
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1/3
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv distribute-lft-out
Counts
4 → 65
Calls
4 calls:
5.0ms
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
87.0ms
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
14.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
17.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
170.0ms
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
130.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
135.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03881007
11398923
25001915

prune331.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

regimes152.0ms

Accuracy

0% (1.5b remaining)

Error of 14.7b against oracle of 13.2b and baseline of 14.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02519
12519

end0.0ms

sample844.0ms

Algorithm
intervals
Results
206.0ms6023×body80valid
175.0ms814×body2560valid
107.0ms639×body1280valid
96.0ms8000×pre80true
40.0ms305×body640valid
14.0ms143×body320valid
5.0ms76×body160valid