Details

Time bar (total: 4.0s)

sample33.0ms

Algorithm
intervals
Results
7.0ms201×body80valid
7.0ms30×body2560valid
4.0ms256×pre80true
3.0ms16×body1280valid
1.0ms5×body640valid
0.0ms3×body320valid
0.0ms1×body160valid

simplify9.0ms

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: 9.8b

localize12.0ms

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))))
0.2b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
18.0b
(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)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (* 4.0 p) p) (* x x))
54.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
73.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify153.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune241.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.6b
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

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:
15.0ms
(- 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)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
46.0ms
(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
51.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03251030
11289956
25001954

prune442.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.7b

localize32.0ms

Local error

Found 4 expressions with local error:

18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
18.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
18.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
124.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
130.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
128.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify66.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0170590
1527553
22131547
35001531

prune446.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

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)))))
2.1b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

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))
15.0ms
(* 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)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (* (* 4.0 p) p) (* x x))
50.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms
(+ 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 (42.0ms)

IterNodesCost
0387817
11913734
25002700

prune241.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.7b

regimes118.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03847
13847

end0.0ms

sample860.0ms

Algorithm
intervals
Results
221.0ms6032×body80valid
195.0ms827×body2560valid
118.0ms606×body1280valid
107.0ms8000×pre80true
43.0ms304×body640valid
16.0ms146×body320valid
6.0ms85×body160valid