Details

Time bar (total: 4.6s)

sample45.0ms

Algorithm
intervals
Results
10.0ms197×body80valid
8.0ms27×body2560valid
8.0ms19×body1280valid
5.0ms256×pre80true
1.0ms5×body640valid
1.0ms5×body320valid
0.0ms3×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 10.9b

Counts
2 → 1

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))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

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:
5.0ms
(+ (* (* 4.0 p) p) (* x x))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* (* 4.0 p) p) (* x x))
52.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify157.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (146.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune277.0ms

Filtered
103 candidates to 79 candidates (76.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New958103
Fresh000
Picked101
Done000
Total968104

Merged error: 10.7b

Counts
104 → 8

localize17.0ms

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)))))
2.6b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
14×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp
7×pow1
5×unswap-sqr
4×expm1-log1p-u fma-def flip3-+ sqrt-div prod-exp flip-+ log1p-expm1-u
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 → 98
Calls
4 calls:
5.0ms
(+ (* (* 4.0 p) p) (* x x))
13.0ms
(* 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)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (* 4.0 p) p) (* x x))
57.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0405866
11987780
25002742

prune451.0ms

Filtered
110 candidates to 79 candidates (71.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1082110
Fresh347
Picked011
Done000
Total1117118

Merged error: 10.7b

Counts
118 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.7b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite24.0ms

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:
9.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
52.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03591348
112631258
250011226

prune350.0ms

Filtered
117 candidates to 88 candidates (75.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1143117
Fresh145
Picked011
Done011
Total1159124

Merged error: 10.7b

Counts
124 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))
5.8b
(+ 1.0 (* x (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
14.1b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.1b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×cbrt-prod
9×associate-*r*
8×sqrt-prod
6×pow1 add-exp-log cbrt-div add-cbrt-cube add-log-exp
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def associate-*l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod
Counts
4 → 76
Calls
4 calls:
10.0ms
(* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* x (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
4.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series581.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))
161.0ms
(+ 1.0 (* x (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
138.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
127.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify63.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04601258
118501149
250011129

prune357.0ms

Filtered
88 candidates to 80 candidates (90.9%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New86288
Fresh066
Picked011
Done022
Total861197

Merged error: 10.7b

Counts
97 → 11

regimes172.0ms

Accuracy

0% (0.4b remaining)

Error of 13.3b against oracle of 12.9b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410

end0.0ms

sample1.1s

Algorithm
intervals
Results
311.0ms6042×body80valid
244.0ms796×body2560valid
152.0ms609×body1280valid
139.0ms8000×pre80true
59.0ms309×body640valid
24.0ms164×body320valid
8.0ms80×body160valid