Details

Time bar (total: 4.7s)

sample35.0ms

Algorithm
intervals
Results
7.0ms188×body80valid
5.0ms27×body1280valid
5.0ms20×body2560valid
4.0ms256×pre80true
1.0ms9×body640valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.1b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
28.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
31.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
267.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
75.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0280888
1816840
22500828
35001827

prune283.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.9b

localize20.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
4.1b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt
6×pow1 sqrt-prod add-log-exp
5×distribute-lft-out
4×unpow-prod-down flip3-+ sqrt-div cube-prod flip-+
3×times-frac associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r/
1×+-commutative frac-2neg prod-exp clear-num sum-log sum-cubes cbrt-unprod div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
85.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
16.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
51.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0296693
11364633
25001630

prune368.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.7b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
10×pow1
9×add-cbrt-cube
6×sqrt-div add-log-exp
5×unswap-sqr
4×flip3-+ prod-exp flip-+
3×sqrt-pow1 associate-*r/ associate-*l*
2×pow1/2 div-exp pow-prod-down associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp 1-exp sum-log un-div-inv *-commutative div-inv
Counts
4 → 88
Calls
4 calls:
3.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
39.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
272.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 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))))))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0390900
11684818
25001784

prune296.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.5b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
4.7b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
23×*-un-lft-identity
22×times-frac
21×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×add-log-exp
5×log-pow unswap-sqr
4×exp-prod sqrt-div prod-exp
3×log-prod flip3-+ associate-*l* flip-+
2×div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ rem-log-exp pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 91
Calls
4 calls:
37.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
272.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
77.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0399963
11665851
25002816

prune341.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

regimes198.0ms

Accuracy

0% (0.5b remaining)

Error of 13.4b against oracle of 13.0b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02814
12814

end0.0ms

sample908.0ms

Algorithm
intervals
Results
229.0ms6013×body80valid
206.0ms869×body2560valid
115.0ms8000×pre80true
115.0ms602×body1280valid
48.0ms314×body640valid
18.0ms137×body320valid
5.0ms65×body160valid