Details

Time bar (total: 3.9s)

sample35.0ms

Algorithm
intervals
Results
7.0ms192×body80valid
6.0ms28×body2560valid
4.0ms21×body1280valid
4.0ms256×pre80true
1.0ms9×body640valid
0.0ms3×body320valid
0.0ms3×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

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:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
13.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
27.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* (* 4.0 p) p) (* x x))
58.0ms
(/ 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)))

simplify111.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0278822
1993772
23998757
35001757

prune256.0ms

Filtered
91 candidates to 67 candidates (73.6%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.2b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
3.0b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×sqrt-div associate-/r* add-log-exp
5×unswap-sqr
4×flip3-+ div-exp prod-exp associate-/r/ flip-+
3×pow-flip associate-*l* associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 122
Calls
4 calls:
33.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
68.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
77.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03671199
116421080
250011018

prune297.0ms

Filtered
134 candidates to 78 candidates (58.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
3.0b
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
16.8b
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×add-exp-log pow-unpow
8×add-log-exp
7×unpow-prod-down associate-*r*
6×add-cbrt-cube
5×pow1
3×distribute-lft-neg-in pow-neg distribute-rgt-neg-in associate-*l* prod-exp unswap-sqr sqr-pow
2×+-commutative neg-sub0 pow-to-exp flip3-+ associate-*r/ pow-exp sum-log flip-+ pow-sub
1×neg-mul-1 pow-pow un-div-inv *-commutative cbrt-unprod
Counts
4 → 76
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
46.0ms
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
3.0ms
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
12.0ms
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

series298.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* (* 4.0 p) p) (* x x))
58.0ms
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
78.0ms
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
128.0ms
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

simplify51.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0362711
11483663
25001662

prune256.0ms

Filtered
88 candidates to 65 candidates (73.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (pow (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))) 3))
0.2b
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
3.0b
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
16.8b
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
10×add-exp-log unpow-prod-down pow-unpow
7×associate-*r*
6×add-cbrt-cube add-log-exp
5×pow1
4×sqr-pow
3×distribute-lft-neg-in pow-neg distribute-rgt-neg-in cube-prod associate-*l* prod-exp unswap-sqr
2×cube-div neg-sub0 pow-to-exp cbrt-div flip3-+ associate-*r/ pow-exp flip-+ pow-sub
1×+-commutative cube-mult neg-mul-1 pow-pow pow1/3 unpow3 sum-log un-div-inv *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 88
Calls
4 calls:
3.0ms
(cbrt (pow (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))) 3))
43.0ms
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
2.0ms
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
11.0ms
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

series348.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(cbrt (pow (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))) 3))
54.0ms
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
80.0ms
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
134.0ms
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

simplify47.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0355959
11384933
25002933

prune303.0ms

Filtered
100 candidates to 72 candidates (72.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.4b

regimes154.0ms

Accuracy

0% (0.6b remaining)

Error of 14.0b against oracle of 13.4b and baseline of 14.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02512
12512

end0.0ms

sample863.0ms

Algorithm
intervals
Results
215.0ms5974×body80valid
194.0ms831×body2560valid
113.0ms606×body1280valid
109.0ms8000×pre80true
48.0ms336×body640valid
22.0ms175×body320valid
6.0ms78×body160valid