Details

Time bar (total: 10.0s)

sample41.0ms

Algorithm
intervals
Results
24.0ms339×body80valid

simplify26.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×add-sqr-sqrt pow1 sub-neg *-un-lft-identity flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt insert-posit16 flip--
Counts
1 → 13
Calls
1 calls:
Slowest
28.0ms
(- (* x.re y.re) (* x.im y.im))

series60.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
60.0ms
(- (* x.re y.re) (* x.im y.im))

simplify908.0ms

Counts
16 → 16

prune137.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

25.3b
(/ (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
1.2b
(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))
0.2b
(* (* x.im y.im) (* x.im y.im))
0.2b
(* (* x.re y.re) (* x.re y.re))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
82×pow1
34×pow-prod-down
30×add-cbrt-cube add-exp-log
16×prod-exp cbrt-unprod
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
8×pow-sqr pow-prod-up
6×add-log-exp
5×difference-of-squares
4×pow-plus insert-posit16 associate-/l*
3×associate-/r*
2×pow2 flip3-- swap-sqr associate-*r* associate-*l* associate-/r/ *-commutative flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
4 → 121
Calls
4 calls:
Slowest
100.0ms
(/ (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
45.0ms
(* (* x.re y.re) (* x.re y.re))
44.0ms
(* (* x.im y.im) (* x.im y.im))
37.0ms
(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))
91.0ms
(/ (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
48.0ms
(* (* x.re y.re) (* x.re y.re))
33.0ms
(* (* x.im y.im) (* x.im y.im))

simplify1.0s

Counts
133 → 133

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b
(sqrt (+ (* x.re y.re) (* x.im y.im)))
0.7b
(sqrt (+ (* x.re y.re) (* x.im y.im)))
0.6b
(/ (- (* x.re y.re) (* x.im y.im)) (sqrt (+ (* x.re y.re) (* x.im y.im))))
0.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* x.re y.re) (* x.im y.im))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
36×*-un-lft-identity times-frac add-cube-cbrt
30×sqrt-prod
12×associate-/r*
9×pow1
8×add-cbrt-cube sqrt-div add-exp-log
6×associate-/l*
5×flip3-+ flip-+
4×associate-/r/ insert-posit16 add-log-exp associate-/l/
3×sqrt-pow1 pow1/2
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg div-exp div-inv pow-div
1×flip3-- div-sub flip--
Counts
4 → 123
Calls
4 calls:
Slowest
49.0ms
(/ (- (* x.re y.re) (* x.im y.im)) (sqrt (+ (* x.re y.re) (* x.im y.im))))
39.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* x.re y.re) (* x.im y.im))))
6.0ms
(sqrt (+ (* x.re y.re) (* x.im y.im)))
6.0ms
(sqrt (+ (* x.re y.re) (* x.im y.im)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
201.0ms
(/ (- (* x.re y.re) (* x.im y.im)) (sqrt (+ (* x.re y.re) (* x.im y.im))))
118.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* x.re y.re) (* x.im y.im))))
108.0ms
(sqrt (+ (* x.re y.re) (* x.im y.im)))
92.0ms
(sqrt (+ (* x.re y.re) (* x.im y.im)))

simplify2.1s

Counts
135 → 135

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes346.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
812.0ms10509×body80valid