Details

Time bar (total: 12.6s)

sample57.0ms

Algorithm
intervals
Results
39.0ms265×body80valid

simplify97.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize21.0ms

Local error

Found 3 expressions with local error:

25.4b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
0.5b
(- (* x.im y.re) (* x.re y.im))
0.0b
(+ (* y.re y.re) (* y.im y.im))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
3 → 67
Calls
3 calls:
Slowest
21.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(- (* x.im y.re) (* x.re y.im))
7.0ms
(+ (* y.re y.re) (* y.im y.im))

series221.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
119.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
70.0ms
(- (* x.im y.re) (* x.re y.im))
33.0ms
(+ (* y.re y.re) (* y.im y.im))

simplify394.0ms

Counts
90 → 76

prune832.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.0b

localize26.0ms

Local error

Found 4 expressions with local error:

27.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.1b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
0.5b
(- (* x.im y.re) (* x.re y.im))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ hypot-def flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
45.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
23.0ms
(- (* x.im y.re) (* x.re y.im))
9.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
70.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
67.0ms
(- (* x.im y.re) (* x.re y.im))
44.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify428.0ms

Counts
141 → 114

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.8b

localize52.0ms

Local error

Found 4 expressions with local error:

27.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.1b
(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
0.5b
(fma x.im y.re (- (* x.re y.im)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
Slowest
10.0ms
(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
0.0ms
(fma x.im y.re (- (* x.re y.im)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
57.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
56.0ms
(fma x.im y.re (- (* x.re y.im)))
53.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify604.0ms

Counts
128 → 105

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.8b

localize41.0ms

Local error

Found 4 expressions with local error:

27.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.1b
(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
0.5b
(fma x.im y.re (- (* x.re y.im)))
0.1b
(/ (/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
98×add-sqr-sqrt
97×*-un-lft-identity add-cube-cbrt
51×sqrt-prod
27×associate-/l*
12×sqrt-div
11×add-cbrt-cube add-exp-log
10×associate-/r/
9×associate-/r*
6×flip3-+ flip-+ div-inv
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef hypot-def associate-/l/
Counts
4 → 191
Calls
4 calls:
Slowest
20.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
20.0ms
(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
18.0ms
(/ (/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
0.0ms
(fma x.im y.re (- (* x.re y.im)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(/ (/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
153.0ms
(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
68.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms
(fma x.im y.re (- (* x.re y.im)))

simplify371.0ms

Counts
297 → 203

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

regimes400.0ms

Accuracy

37.6% (6.8b remaining)

Error of 12.8b against oracle of 6.0b and baseline of 16.9b

bsearch140.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8453×body80valid