Details

Time bar (total: 3.7s)

sample38.0ms

Algorithm
intervals
Results
7.0ms31×body2560valid
6.0ms172×body80valid
5.0ms26×body1280valid
4.0ms256×pre80true
2.0ms14×body640valid
1.0ms7×body320valid
0.0ms6×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

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))))
1.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite33.0ms

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))))
13.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* (* 4.0 p) p) (* x x))
57.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
80.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify150.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (141.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune312.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.9b

localize12.0ms

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)))))
4.8b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

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))
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)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (* 4.0 p) p) (* x x))
56.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify53.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0405866
11987780
25002742

prune319.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(* x (/ 1 (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))))
4.8b
(+ 1.0 (* x (/ 1 (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x)))))))
12.9b
(sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
18×associate-*r*
15×*-un-lft-identity
14×add-cube-cbrt times-frac
13×add-exp-log
9×pow1 add-cbrt-cube
8×add-log-exp
5×associate-*r/
4×expm1-log1p-u fma-def flip3-+ sqrt-div prod-exp sqrt-prod flip-+ log1p-expm1-u
3×associate-*l* unswap-sqr
2×+-commutative sqrt-pow1 div-exp pow-prod-down sum-log associate-/r/ cbrt-unprod
1×cbrt-undiv rec-exp pow1/2 1-exp un-div-inv *-commutative div-inv
Counts
4 → 88
Calls
4 calls:
5.0ms
(+ (* (* 4.0 p) p) (* x x))
15.0ms
(* x (/ 1 (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))

series218.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (* 4.0 p) p) (* x x))
56.0ms
(* x (/ 1 (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))))
76.0ms
(+ 1.0 (* x (/ 1 (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms
(sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))

simplify61.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0406823
12173724
25001684

prune303.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.9b

localize17.0ms

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))))
1.6b
(+ 1.0 (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

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))))
15.0ms
(+ 1.0 (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* (* 4.0 p) p) (* x x))
52.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0301885
11174819
25001804

prune302.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.9b

regimes155.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02310
12310

end0.0ms

sample832.0ms

Algorithm
intervals
Results
218.0ms6084×body80valid
184.0ms798×body2560valid
110.0ms608×body1280valid
104.0ms8000×pre80true
41.0ms298×body640valid
14.0ms130×body320valid
6.0ms82×body160valid