Details

Time bar (total: 4.4s)

sample42.0ms

Algorithm
intervals
Results
9.0ms188×body80valid
8.0ms27×body2560valid
5.0ms20×body1280valid
5.0ms256×pre80true
2.0ms10×body640valid
1.0ms9×body320valid
0.0ms2×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.5b

Counts
2 → 1

localize14.0ms

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))))
1.0b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

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:
12.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
278.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
51.0ms
(/ 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)))

simplify72.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0280888
1816840
22500828
35001827

prune249.0ms

Filtered
93 candidates to 71 candidates (76.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New831093
Fresh000
Picked101
Done000
Total841094

Merged error: 14.2b

Counts
94 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
3.5b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

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:
37.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
53.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0296693
11364633
25001630

prune313.0ms

Filtered
82 candidates to 64 candidates (78.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New81182
Fresh189
Picked101
Done000
Total83992

Merged error: 14.2b

Counts
92 → 9

localize16.0ms

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))))
3.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×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×flip3-+ div-exp prod-exp associate-/r/ flip-+
3×pow-flip 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 → 122
Calls
4 calls:
13.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.0ms
(/ 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)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03671199
116421080
250011018

prune253.0ms

Filtered
134 candidates to 80 candidates (59.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1313134
Fresh088
Picked101
Done000
Total13211143

Merged error: 14.2b

Counts
143 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))))
0.2b
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
3.6b
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
15.9b
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×add-exp-log pow-unpow
8×pow1
7×unpow-prod-down associate-*r*
6×add-cbrt-cube add-log-exp
4×associate-*r/
3×distribute-lft-neg-in pow-neg distribute-rgt-neg-in associate-*l* prod-exp unswap-sqr sqr-pow
2×neg-sub0 pow-to-exp sqrt-pow1 flip3-+ sqrt-div pow-exp flip-+ pow-sub
1×+-commutative neg-mul-1 pow-pow pow1/2 pow-prod-down sum-log sqrt-prod un-div-inv *-commutative cbrt-unprod
Counts
4 → 78
Calls
4 calls:
4.0ms
(sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))))
13.0ms
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
3.0ms
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
6.0ms
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

series545.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(sqrt (* 0.5 (+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))))
57.0ms
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
76.0ms
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
141.0ms
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

simplify166.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0317794
11063747
24595747
35002747

prune209.0ms

Filtered
90 candidates to 69 candidates (76.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New88290
Fresh3710
Picked101
Done000
Total929101

Merged error: 14.2b

Counts
101 → 9

regimes118.0ms

Accuracy

0% (0.5b remaining)

Error of 13.5b against oracle of 13.0b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02412
12412

end0.0ms

sample1.1s

Algorithm
intervals
Results
303.0ms6048×body80valid
251.0ms790×body2560valid
155.0ms610×body1280valid
144.0ms8000×pre80true
60.0ms299×body640valid
26.0ms167×body320valid
8.0ms86×body160valid

Profiling

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