Details

Time bar (total: 10.8s)

sample16.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms105×body80nan

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
056
175
done75

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) y)
21.1b
(sqrt (+ (* x x) y))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative rem-sqrt-square fma-def sqrt-pow1 pow1/2 sum-log hypot-def
Counts
2 → 32
Calls
2 calls:
3.0ms
(+ (* x x) y)
5.0ms
(sqrt (+ (* x x) y))

series79.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(+ (* x x) y)
49.0ms
(sqrt (+ (* x x) y))

simplify2.7s

Counts
38 → 38
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
063345
1152284
2426250
31291248
44278247
done5000247

prune97.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (* (* (cbrt (fma x x y)) (cbrt (fma x x y))) (cbrt (fma x x y))))
21.9b
(cbrt (fma x x y))
21.9b
(cbrt (fma x x y))
21.9b
(cbrt (fma x x y))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
15×sqrt-pow1
12×pow1/3
9×cbrt-prod pow-prod-up
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 65
Calls
4 calls:
11.0ms
(sqrt (* (* (cbrt (fma x x y)) (cbrt (fma x x y))) (cbrt (fma x x y))))
0.0ms
(cbrt (fma x x y))
0.0ms
(cbrt (fma x x y))
1.0ms
(cbrt (fma x x y))

series377.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (* (* (cbrt (fma x x y)) (cbrt (fma x x y))) (cbrt (fma x x y))))
106.0ms
(cbrt (fma x x y))
104.0ms
(cbrt (fma x x y))
109.0ms
(cbrt (fma x x y))

simplify1.6s

Counts
77 → 77
Iterations

Useful iterations: done (1.6s)

IterNodesCost
077768
1148662
2295512
3695471
41783470
done5001469

prune208.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma 1/2 (/ y x) x)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma 1/2 (/ y x) x)

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(fma 1/2 (/ y x) x)

simplify2.3s

Counts
13 → 13
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
016110
121107
24795
312895
445595
5181295
done500095

prune30.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma 1/2 (/ y x) x)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma 1/2 (/ y x) x)

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(fma 1/2 (/ y x) x)

simplify2.6s

Counts
13 → 13
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
016110
121107
24795
312895
445595
5181295
done500095

prune27.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 21.2b

bsearch59.0ms

Steps
ItersRangePoint
6
3.05690573887077e+112
2.2882387430117383e+113
7.4055700216532296e+112
9
-9.454570341338981e+157
-2.2087357092495854e+152
-1.3614720717698548e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01527
11627
done1627

end0.0ms

sample379.0ms

Algorithm
intervals
Results
161.0ms8000×body80valid
45.0ms2617×body80nan