Details

Time bar (total: 4.1s)

sample48.0ms

Algorithm
intervals
Results
9.0ms182×body80valid
8.0ms30×body2560valid
5.0ms256×pre80true
4.0ms23×body640valid
3.0ms14×body1280valid
1.0ms5×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: 15.9b

localize16.0ms

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))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite123.0ms

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:
28.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms
(+ (* (* 4.0 p) p) (* x x))
54.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
34.0ms
(+ (* (* 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)))

simplify145.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune253.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.6b

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)))))
4.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite119.0ms

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:
16.0ms
(+ (* (* 4.0 p) p) (* x x))
71.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* (* 4.0 p) p) (* x x))
55.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
77.0ms
(+ 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

prune266.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.2b
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
39×sqrt-prod
27×associate-*r*
22×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac
11×pow1
10×sqrt-div
9×add-exp-log add-cbrt-cube
6×add-log-exp
4×flip3-+ flip-+
3×associate-*r/ pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×+-commutative frac-times associate-*l* associate-*l/ sum-log *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
150.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
71.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03861299
115091123
250011062

prune333.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (pow (+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0) 3))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.4b
(+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0)
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
24×*-un-lft-identity associate-*r*
22×add-cube-cbrt times-frac
14×sqrt-prod
13×add-exp-log
12×cbrt-prod
9×add-cbrt-cube
7×pow1
6×add-log-exp
5×unswap-sqr
4×flip3-+ sqrt-div prod-exp flip-+
3×unpow-prod-down cube-prod associate-*l*
2×cube-div cbrt-div div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative cube-mult rem-sqrt-square rec-exp sqrt-pow1 pow1/2 pow1/3 1-exp unpow3 associate-*r/ pow-prod-down sum-log un-div-inv *-commutative rem-cbrt-cube div-inv sqr-pow
Counts
4 → 98
Calls
4 calls:
45.0ms
(cbrt (pow (+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0) 3))
68.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
26.0ms
(+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0)
21.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(cbrt (pow (+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0) 3))
55.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms
(+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0)
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04251050
11936996
25001972

prune294.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.6b

regimes200.0ms

Accuracy

0% (0.5b remaining)

Error of 13.6b against oracle of 13.2b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02813
12813

end0.0ms

sample804.0ms

Algorithm
intervals
Results
193.0ms6014×body80valid
166.0ms814×body2560valid
98.0ms601×body1280valid
92.0ms8000×pre80true
46.0ms344×body640valid
14.0ms156×body320valid
4.0ms71×body160valid