Details

sample51.0ms

Algorithm

intervals

Results

23.0ms

271×

body

valid

simplify55.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
24.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

9.0ms	(+ (* y.re y.re) (* y.im y.im))
28.0ms	(- (* x.im y.re) (* x.re y.im))
43.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series283.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (* y.re y.re) (* y.im y.im))
74.0ms	(- (* x.im y.re) (* x.re y.im))
158.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify713.0ms

Counts: 64 → 64

prune291.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

9.0ms	(- (* x.im y.re) (* x.re y.im))
46.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* x.im y.re) (* x.re y.im))
148.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
56.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts: 98 → 98

prune428.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.4b

localize19.0ms

Local error

Found 4 expressions with local error:

11.1b	(/ (* x.im y.re) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
7×	`pow1`
6×	`times-frac` `associate-/r*`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

37.0ms	(/ (* x.im y.re) (sqrt (+ (* y.re y.re) (* y.im y.im))))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
19.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (* x.im y.re) (sqrt (+ (* y.re y.re) (* y.im y.im))))
64.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
71.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts: 86 → 86

prune391.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.1b

localize34.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
44.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts: 72 → 72

prune467.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.1b

regimes283.0ms

Accuracy

-88.9% (3.2b remaining)

Error of 25.8b against oracle of 22.6b and baseline of 24.3b

bsearch0.0ms

simplify1.6s

end0.0ms

sample1.3s

Algorithm

intervals

Results

755.0ms

8497×

body

valid