Details

Time bar (total: 9.8s)

sample56.0ms

Algorithm
intervals
Results
13.0ms192×body80valid
11.0ms25×body2560valid
7.0ms256×pre80true
7.0ms19×body1280valid
4.0ms13×body640valid
1.0ms4×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize14.0ms

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))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×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×expm1-log1p-u fma-def flip3-+ sqrt-div flip-+ log1p-expm1-u
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 → 91
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
11.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify147.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (138.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune899.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.9b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
24×add-sqr-sqrt
23×add-cube-cbrt
18×times-frac
15×sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×log-pow
4×expm1-log1p-u log-prod exp-prod sqrt-div log1p-expm1-u
3×fma-def flip3-+ flip-+ associate-/l*
2×associate-/r/ distribute-lft-out
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp exp-sum clear-num sum-log div-inv
Counts
4 → 96
Calls
4 calls:
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
97.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify73.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0286956
1875889
22480876
35002874

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.1b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
31×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 105
Calls
4 calls:
13.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series50.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03591348
112631258
250011226

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- x) (- (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.1b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (- x) (- (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
220×times-frac
204×sqrt-prod
168×distribute-lft-neg-in distribute-rgt-neg-in
155×add-sqr-sqrt
153×add-cube-cbrt *-un-lft-identity
34×neg-mul-1
22×associate-/r*
10×associate-/l*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def distribute-frac-neg
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ distribute-rgt-neg-out distribute-neg-frac
1×cbrt-undiv +-commutative neg-sub0 frac-2neg div-sub div-exp unsub-neg clear-num sum-log div-inv
Counts
4 → 322
Calls
4 calls:
29.0ms
(/ (- x) (- (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
2.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (- x) (- (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series50.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ (- x) (- (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (- x) (- (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify105.0ms

Algorithm
egg-herbie
Counts
334 → 334
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
08375463
130895313
250025193

prune3.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

regimes513.0ms

Accuracy

0% (1.1b remaining)

Error of 14.1b against oracle of 13.0b and baseline of 14.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03020
13420
23720
33920
43920

end0.0ms

sample1.4s

Algorithm
intervals
Results
397.0ms6047×body80valid
335.0ms787×body2560valid
221.0ms8000×pre80true
199.0ms581×body1280valid
84.0ms315×body640valid
33.0ms163×body320valid
14.0ms107×body160valid