Details

Time bar (total: 4.4s)

sample37.0ms

Algorithm
intervals
Results
8.0ms35×body2560valid
7.0ms187×body80valid
4.0ms256×pre80true
4.0ms21×body1280valid
1.0ms9×body640valid
0.0ms2×body320valid
0.0ms2×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

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))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

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))
8.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
17.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* (* 4.0 p) p) (* x x))
62.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
82.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify160.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (150.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune326.0ms

Filtered
103 candidates to 79 candidates (76.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.8b
(/ x (fma (* 4.0 p) p (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
80×*-un-lft-identity
78×add-cube-cbrt
72×prod-diff
65×times-frac
34×sqrt-prod
10×sqrt-div
6×pow1 add-exp-log associate-/r/ add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u div-inv
3×fma-neg associate-/r* associate-/l* difference-of-squares
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- distribute-lft-out--
Counts
4 → 156
Calls
4 calls:
16.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(/ x (fma (* 4.0 p) p (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
63.0ms
(/ x (fma (* 4.0 p) p (* x x)))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
65.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify81.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
06824617
122563256
250012931

prune635.0ms

Filtered
168 candidates to 94 candidates (56.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.3b

localize26.0ms

Local error

Found 4 expressions with local error:

15.2b
(sqrt (fma (* 4.0 p) p (* x x)))
15.2b
(sqrt (fma (* 4.0 p) p (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp
2×flip3-+ flip-+
Counts
4 → 64
Calls
4 calls:
2.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
71.0ms
(sqrt (fma (* 4.0 p) p (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify89.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0123410
1340394
2980394
32540394
45001394

prune479.0ms

Filtered
76 candidates to 68 candidates (89.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

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)))))
3.0b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

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))
15.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (* (* 4.0 p) p) (* x x))
56.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
84.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
64.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0405866
11987780
25002742

prune312.0ms

Filtered
110 candidates to 81 candidates (73.6%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.3b

regimes175.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03131
13131

end0.0ms

sample858.0ms

Algorithm
intervals
Results
223.0ms6040×body80valid
176.0ms781×body2560valid
118.0ms604×body1280valid
109.0ms8000×pre80true
47.0ms329×body640valid
16.0ms156×body320valid
6.0ms90×body160valid