Details

Time bar (total: 5.2s)

sample35.0ms

Algorithm
intervals
Results
7.0ms192×body80valid
5.0ms24×body2560valid
4.0ms25×body1280valid
4.0ms256×pre80true
1.0ms10×body640valid
0.0ms4×body320valid
0.0ms1×body160valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539
done539

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity add-log-exp
6×add-sqr-sqrt
5×add-cube-cbrt
4×pow1 fma-def
3×add-exp-log expm1-log1p-u flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×+-commutative sqrt-div sum-log
1×rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out
Counts
3 → 48
Calls
3 calls:
16.0ms
(+ (* (* 4.0 p) p) (* x x))
54.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series173.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ (* (* 4.0 p) p) (* x x))
80.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Counts
57 → 57
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0219397
1816366
23002361
35001357
done5001357

prune182.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.1b

localize18.0ms

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)))))
6.8b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite235.0ms

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:
117.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
68.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
81.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify57.0ms

Counts
148 → 148
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03051424
111511313
250011274
done50011274

prune379.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.1b

localize23.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
23.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
140.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
134.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
136.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

Counts
74 → 74
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0180637
1573596
22310587
35001571
done5001571

prune494.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.1b

localize30.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 64
Calls
4 calls:
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
135.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
129.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify67.0ms

Counts
76 → 76
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0180606
1573572
22310566
35001554
done5001554

prune484.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.1b

regimes593.0ms

Accuracy

0% (0.2b remaining)

Error of 13.8b against oracle of 13.5b and baseline of 13.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0199
1199
done199

end0.0ms

sample884.0ms

Algorithm
intervals
Results
207.0ms5975×body80valid
183.0ms831×body2560valid
118.0ms632×body1280valid
102.0ms8000×pre80true
49.0ms344×body640valid
15.0ms150×body320valid
7.0ms68×body160valid