Details

Time bar (total: 4.1s)

sample21.0ms

Algorithm
intervals
Results
8.0ms327×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0123
1203
2243
3243
done243

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt sub-neg flip3-- *-un-lft-identity fma-neg diff-log prod-diff add-cbrt-cube flip-- log1p-expm1-u
Counts
1 → 16
Calls
1 calls:
8.0ms
(- (* x.re y.re) (* x.im y.im))

series39.0ms

Counts
1 → 3
Calls
1 calls:
39.0ms
(- (* x.re y.re) (* x.im y.im))

simplify79.0ms

Counts
19 → 19
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
010592
136283
2110783
3262280
4500180
done500180

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

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

series48.0ms

Counts
1 → 3
Calls
1 calls:
48.0ms
(fma x.re y.re (- (* x.im y.im)))

simplify121.0ms

Counts
13 → 13
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03055
15948
219748
376448
4422548
5500148
done500148

prune29.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x.re y.re) (* x.im y.im))
0.2b
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
0.8b
(sqrt (- (* x.re y.re) (* x.im y.im)))
0.8b
(sqrt (- (* x.re y.re) (* x.im y.im)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-- flip--
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×expm1-log1p-u frac-times log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 sub-neg pow-plus fma-neg sqrt-unprod diff-log prod-diff prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
8.0ms
(- (* x.re y.re) (* x.im y.im))
50.0ms
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
10.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
13.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* x.re y.re) (* x.im y.im))
39.0ms
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
91.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
93.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))

simplify41.0ms

Counts
121 → 121
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0270826
1994750
25001724
done5001724

prune234.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (* x.re y.re) (* x.im y.im))
12.4b
(/ (* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))) (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))))))
15.7b
(sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))
25.3b
(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)))))

rewrite363.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
18×pow1 sqrt-div sqrt-prod
17×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt
9×prod-exp cbrt-unprod
8×pow-prod-down associate-/l/
7×flip3-- flip--
6×times-frac associate-/r*
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp difference-of-squares sqr-pow
2×cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ div-exp associate-*l/ associate-/r/ flip-+
1×difference-cubes sqrt-undiv frac-2neg sqrt-unprod associate-*r* associate-*l* clear-num *-commutative hypot-def div-inv associate-/l* distribute-lft-out--
Counts
4 → 105
Calls
4 calls:
26.0ms
(* (* x.re y.re) (* x.im y.im))
164.0ms
(/ (* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))) (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))))))
27.0ms
(sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))
144.0ms
(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)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* x.re y.re) (* x.im y.im))
232.0ms
(/ (* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))) (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))))))
1.0s
(sqrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3)))
114.0ms
(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)))))

simplify83.0ms

Counts
117 → 117
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
05001812
122681661
250011654
done50011654

prune591.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes103.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0123
1143
2143
done143

end0.0ms

sample530.0ms

Algorithm
intervals
Results
197.0ms10439×body80valid