Details

Time bar (total: 4.5s)

sample34.0ms

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

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: 12.6b

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)))

rewrite59.0ms

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))))
29.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* (* 4.0 p) p) (* x x))
53.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify150.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (140.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune303.0ms

Filtered
103 candidates to 79 candidates (76.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.4b

localize17.0ms

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)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
40×times-frac
37×*-un-lft-identity
35×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×expm1-log1p-u flip3-+ div-exp prod-exp associate-/r/ flip-+ log1p-expm1-u
3×pow-flip fma-def 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 → 133
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))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
70.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
82.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03841256
117101134
250011063

prune468.0ms

Filtered
145 candidates to 89 candidates (61.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
7.8b
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
46×sqrt-prod
38×add-sqr-sqrt
27×associate-*r*
24×*-un-lft-identity
22×add-cube-cbrt times-frac
8×pow1
7×sqrt-div
6×add-exp-log add-cbrt-cube add-log-exp unswap-sqr
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×+-commutative associate-*r/ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod div-inv
Counts
4 → 100
Calls
4 calls:
38.0ms
(* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
2.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (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)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
74.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (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)))

simplify51.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03931169
114691054
25002975

prune377.0ms

Filtered
112 candidates to 86 candidates (76.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
5.4b
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
17.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
17.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt
9×times-frac
6×add-exp-log cbrt-prod add-cbrt-cube add-log-exp
4×pow1 expm1-log1p-u cbrt-div log1p-expm1-u
3×fma-def flip3-+ associate-/r* flip-+ associate-/l*
2×pow1/3
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv distribute-lft-out
Counts
4 → 76
Calls
4 calls:
2.0ms
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
51.0ms
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
152.0ms
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
129.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
128.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04061075
11472979
25002968

prune371.0ms

Filtered
88 candidates to 80 candidates (90.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.4b

regimes247.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0199
1199

end0.0ms

sample826.0ms

Algorithm
intervals
Results
206.0ms5974×body80valid
181.0ms831×body2560valid
109.0ms606×body1280valid
105.0ms8000×pre80true
48.0ms336×body640valid
18.0ms175×body320valid
5.0ms78×body160valid