Details

Time bar (total: 22.1s)

sample34.0ms

Algorithm
intervals
Results
23.0ms322×body80valid

simplify33.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
33.0ms
(- (* x.re y.re) (* x.im y.im))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* x.re y.re) (* x.im y.im))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×add-sqr-sqrt expm1-log1p-u pow1 sub-neg *-un-lft-identity flip3-- add-cbrt-cube fma-neg diff-log prod-diff add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u flip--
Counts
1 → 17
Calls
1 calls:
Slowest
8.0ms
(- (* x.re y.re) (* x.im y.im))

series45.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
45.0ms
(- (* x.re y.re) (* x.im y.im))

simplify248.0ms

Counts
6 → 20
Calls
6 calls:
Slowest
177.0ms
(/ (exp (* x.re y.re)) (exp (* x.im y.im)))
18.0ms
(- (* y.re x.re) (* y.im x.im))
17.0ms
(fma x.re y.re (- (* y.im x.im)))
16.0ms
(fma (- y.im) x.im (* y.im x.im))
16.0ms
(- (* y.re x.re) (* y.im x.im))

prune182.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma x.re y.re (- (* x.im y.im)))

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
1 → 11
Calls
1 calls:
Slowest
0.0ms
(fma x.re y.re (- (* x.im y.im)))

series45.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
45.0ms
(fma x.re y.re (- (* x.im y.im)))

simplify70.0ms

Counts
3 → 14
Calls
3 calls:
Slowest
37.0ms
(- (* y.re x.re) (* y.im x.im))
31.0ms
(- (* y.re x.re) (* y.im x.im))
1.0ms
0

prune120.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (- (* x.re y.re) (* x.im y.im)))
1.0b
(sqrt (- (* x.re y.re) (* x.im y.im)))
0.3b
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
0.0b
(- (* x.re y.re) (* x.im y.im))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
9×flip3-- flip--
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log add-log-exp
5×pow-prod-up
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*l/ associate-*r/
1×pow2 sub-neg rem-square-sqrt pow-plus fma-neg sqrt-unprod diff-log prod-diff prod-exp *-commutative cbrt-unprod
Counts
4 → 113
Calls
4 calls:
Slowest
44.0ms
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
18.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
17.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
11.0ms
(- (* x.re y.re) (* x.im y.im))

series348.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
102.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
73.0ms
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
67.0ms
(- (* x.re y.re) (* x.im y.im))

simplify6.8s

Counts
102 → 125
Calls
102 calls:
Slowest
427.0ms
(* (* (* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im)))) (sqrt (- (* x.re y.re) (* x.im y.im)))) (* (* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im)))) (sqrt (- (* x.re y.re) (* x.im y.im)))))
417.0ms
(sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))
384.0ms
(sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im)))))
363.0ms
(sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))
342.0ms
(* (sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im))))) (sqrt (+ (* x.re y.re) (* x.im y.im))))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (- (* x.re y.re) (* x.im y.im)))
1.0b
(sqrt (- (* x.re y.re) (* x.im y.im)))
1.0b
(sqrt (- (* x.re y.re) (* x.im y.im)))
0.3b
(* (sqrt (sqrt (- (* x.re y.re) (* x.im y.im)))) (sqrt (sqrt (- (* x.re y.re) (* x.im y.im)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
52×add-sqr-sqrt
35×sqrt-pow1
30×pow1 sqrt-div
19×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×flip3-- associate-*r* associate-*l* pow-prod-up flip-- unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square
2×associate-*l/ associate-*r/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 140
Calls
4 calls:
Slowest
60.0ms
(* (sqrt (sqrt (- (* x.re y.re) (* x.im y.im)))) (sqrt (sqrt (- (* x.re y.re) (* x.im y.im)))))
23.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
18.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
18.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
125.0ms
(* (sqrt (sqrt (- (* x.re y.re) (* x.im y.im)))) (sqrt (sqrt (- (* x.re y.re) (* x.im y.im)))))
116.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
105.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))

simplify8.5s

Counts
151 → 152
Calls
151 calls:
Slowest
461.0ms
(sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))
416.0ms
(sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))
391.0ms
(sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))
338.0ms
(* (sqrt (sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im)))))) (sqrt (sqrt (+ (* x.re y.re) (* x.im y.im)))))
318.0ms
(* (sqrt (sqrt (+ (* x.re y.re) (* x.im y.im)))) (sqrt (sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im)))))))

prune1.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes412.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s10495×body80valid