Details

Time bar (total: 4.6s)

sample40.0ms

Algorithm
intervals
Results
11.0ms187×body80valid
8.0ms35×body2560valid
4.0ms256×pre80true
4.0ms21×body1280valid
1.0ms9×body640valid
0.0ms2×body320valid
0.0ms2×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize11.0ms

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))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b
(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)))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* (* 4.0 p) p) (* x x))
54.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify147.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune267.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.4b
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

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:
12.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
48.0ms
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms
(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

prune492.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.3b

localize27.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (/ (pow x 2) (+ (* (* 4.0 p) p) (* x x))))
15.0b
(cbrt (/ (pow x 2) (+ (* (* 4.0 p) p) (* x x))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-prod
48×times-frac
38×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity
18×unpow-prod-down
6×pow1 sqrt-prod unpow2 sqr-pow
4×add-exp-log flip3-+ sqrt-div associate-/r/ add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 pow1/3 div-inv
Counts
4 → 108
Calls
4 calls:
7.0ms
(cbrt (/ (pow x 2) (+ (* (* 4.0 p) p) (* x x))))
8.0ms
(cbrt (/ (pow x 2) (+ (* (* 4.0 p) p) (* x x))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(cbrt (/ (pow x 2) (+ (* (* 4.0 p) p) (* x x))))
129.0ms
(cbrt (/ (pow x 2) (+ (* (* 4.0 p) p) (* x x))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify144.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
02701464
18831372
240791362
350031358

prune839.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

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)))))
3.0b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

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))
14.0ms
(* 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)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (* (* 4.0 p) p) (* x x))
54.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0387817
11913734
25002700

prune258.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.3b

regimes182.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03544
13544

end0.0ms

sample856.0ms

Algorithm
intervals
Results
226.0ms6040×body80valid
181.0ms781×body2560valid
109.0ms604×body1280valid
102.0ms8000×pre80true
51.0ms329×body640valid
17.0ms156×body320valid
6.0ms90×body160valid