Details

Time bar (total: 4.3s)

sample34.0ms

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

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize16.0ms

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)))

rewrite34.0ms

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))))
13.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (* (* 4.0 p) p) (* x x))
64.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify158.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (148.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune317.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.8b
(/ x (fma (* 4.0 p) p (* x x)))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

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)))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms
(/ x (fma (* 4.0 p) p (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify83.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06824619
122563256
250022931

prune622.0ms

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
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:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
14.0ms
(* 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)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* (* 4.0 p) p) (* x x))
55.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
81.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0405866
11987780
25002742

prune333.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.2b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
21×*-un-lft-identity
19×add-cube-cbrt
18×pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times log1p-expm1-u
3×fma-def
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 136
Calls
4 calls:
18.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* 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)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
86.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify61.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03051424
111511313
250011274

prune392.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.7b

regimes139.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02925
12925

end0.0ms

sample858.0ms

Algorithm
intervals
Results
223.0ms6032×body80valid
194.0ms827×body2560valid
109.0ms606×body1280valid
108.0ms8000×pre80true
43.0ms304×body640valid
15.0ms146×body320valid
8.0ms85×body160valid