Details

sample33.0ms

Algorithm

intervals

Results

11.0ms

270×

body

valid

simplify62.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.4b	(- (* x.im y.re) (* x.re y.im))
23.1b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite73.0ms

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:

13.0ms	(+ (* y.re y.re) (* y.im y.im))
13.0ms	(- (* x.im y.re) (* x.re y.im))
44.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ (* y.re y.re) (* y.im y.im))
65.0ms	(- (* x.im y.re) (* x.re y.im))
146.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts: 64 → 64

prune274.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* x.im y.re) (* x.re y.im))
13.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite92.0ms

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:

14.0ms	(- (* x.im y.re) (* x.re y.im))
53.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* x.im y.re) (* x.re y.im))
152.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts: 98 → 98

prune388.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.6b

localize32.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))
14.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip--` `flip-+`

Counts

4 → 56

Calls

4 calls:

12.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
6.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
171.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.4s

Counts: 68 → 68

prune417.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 21.6b

localize39.0ms

Local error

Found 4 expressions with local error:

13.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.9b	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
18×	`cbrt-prod` `times-frac`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `unpow-prod-down` `cube-prod` `associate-/r*` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`cube-div` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `flip3--` `frac-2neg` `pow1/3` `unpow3` `div-sub` `div-exp` `clear-num` `flip--` `rem-cbrt-cube` `div-inv` `sqr-pow`

Counts

4 → 103

Calls

4 calls:

46.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
23.0ms	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

series354.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
61.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

simplify765.0ms

Counts: 115 → 115

prune620.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 21.6b

regimes332.0ms

Accuracy

-3.7% (2.1b remaining)

Error of 26.1b against oracle of 23.9b and baseline of 26.0b

bsearch0.0ms

simplify157.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

684.0ms

8477×

body

valid