Details

Time bar (total: 3.9s)

sample35.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize14.0ms

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)))

rewrite54.0ms

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))))
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (* (* 4.0 p) p) (* x x))
53.0ms
(/ 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)))

simplify144.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune324.0ms

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)))

rewrite55.0ms

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))
34.0ms
(* x (/ 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)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* (* 4.0 p) p) (* x x))
56.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
77.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify68.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0405866
11987780
25002742

prune333.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.9b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:
3.0ms
(+ (* x x) (* (* 4.0 p) p))
19.0ms
(* x (/ 1 (sqrt (+ (* x x) (* (* 4.0 p) p)))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* x x) (* (* 4.0 p) p))))))
3.0ms
(sqrt (+ (* x x) (* (* 4.0 p) p)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* x x) (* (* 4.0 p) p))
54.0ms
(* x (/ 1 (sqrt (+ (* x x) (* (* 4.0 p) p)))))
77.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* x x) (* (* 4.0 p) p))))))
56.0ms
(sqrt (+ (* x x) (* (* 4.0 p) p)))

simplify52.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0403863
12007777
25001737

prune318.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.9b

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)))))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

rewrite100.0ms

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:
52.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

series250.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
79.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03051424
111511313
250011274

prune367.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.9b

regimes151.0ms

Accuracy

0% (0.5b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410

end0.0ms

sample796.0ms

Algorithm
intervals
Results
201.0ms6084×body80valid
170.0ms798×body2560valid
106.0ms8000×pre80true
103.0ms608×body1280valid
47.0ms298×body640valid
13.0ms130×body320valid
5.0ms82×body160valid