Details

Time bar (total: 15.9s)

sample55.0ms

Algorithm
intervals
Results
37.0ms268×body80valid

simplify29.0ms

Counts
1 → 1

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.5b

localize47.0ms

Local error

Found 3 expressions with local error:

27.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
1.0b
(+ (* x.re y.re) (* x.im y.im))
0.0b
(+ (* y.re y.re) (* y.im y.im))

rewrite82.0ms

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
4×flip3-+ flip-+
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l*
2×+-commutative sum-log fma-def associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
3 → 64
Calls
3 calls:
Slowest
51.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
20.0ms
(+ (* y.re y.re) (* y.im y.im))
10.0ms
(+ (* x.re y.re) (* x.im y.im))

series178.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
84.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
48.0ms
(+ (* y.re y.re) (* y.im y.im))
45.0ms
(+ (* x.re y.re) (* x.im y.im))

simplify383.0ms

Counts
83 → 73

prune843.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.1b

localize51.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
1.0b
(+ (* x.re y.re) (* x.im y.im))

rewrite52.0ms

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
5×flip3-+ flip-+
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log fma-def frac-2neg div-exp div-inv
Counts
4 → 99
Calls
4 calls:
Slowest
30.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms
(+ (* x.re y.re) (* x.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)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
57.0ms
(+ (* x.re y.re) (* x.im y.im))
51.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify307.0ms

Counts
134 → 111

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.6b

localize37.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
1.0b
(+ (* x.re y.re) (* x.im y.im))
0.1b
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))

rewrite134.0ms

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*
8×flip3-+ flip-+
6×div-inv add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×associate-/l/
2×clear-num frac-2neg
1×+-commutative rem-sqrt-square sum-log fma-def sqrt-pow1 pow1/2 hypot-def
Counts
4 → 197
Calls
4 calls:
Slowest
61.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
44.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms
(+ (* x.re y.re) (* x.im y.im))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series470.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
147.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
55.0ms
(+ (* x.re y.re) (* x.im y.im))
51.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify413.0ms

Counts
303 → 209

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize32.0ms

Local error

Found 4 expressions with local error:

17.6b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))
0.3b
(fma x.re y.re (* x.im y.im))
0.2b
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
0.1b
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 323
Calls
4 calls:
Slowest
16.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))
13.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
5.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))
0.0ms
(fma x.re y.re (* x.im y.im))

series612.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
256.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))
161.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
133.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))
62.0ms
(fma x.re y.re (* x.im y.im))

simplify977.0ms

Counts
517 → 335

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

regimes390.0ms

Accuracy

33.4% (7.3b remaining)

Error of 13.2b against oracle of 5.9b and baseline of 16.9b

bsearch113.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.1s8453×body80valid