Details

sample46.0ms

Algorithm

intervals

Results

21.0ms

267×

body

valid

simplify28.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(+ (* x.re y.re) (* x.im y.im))
22.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite98.0ms

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`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

9.0ms	(+ (* y.re y.re) (* y.im y.im))
13.0ms	(+ (* x.re y.re) (* x.im y.im))
74.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* y.re y.re) (* y.im y.im))
47.0ms	(+ (* x.re y.re) (* x.im y.im))
121.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts: 62 → 62

prune261.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

76.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
56.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
178.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
65.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts: 276 → 276

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.6b

localize32.0ms

Local error

Found 4 expressions with local error:

9.4b	(* (/ 1 (* 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
26.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.3b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
27.3b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-exp-log`
40×	`add-sqr-sqrt`
33×	`times-frac` `associate-r`
32×	`prod-exp`
28×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-cbrt-cube`
23×	`sqrt-prod`
22×	`div-exp`
16×	`cbrt-prod`
12×	`1-exp`
8×	`cbrt-unprod`
7×	`pow1` `cbrt-undiv` `associate-l`
6×	`rec-exp` `cbrt-div`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp` `unswap-sqr`
2×	`pow1/3` `associate-/r/` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 123

Calls

4 calls:

151.0ms	(* (/ 1 (* 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series1.1s

Counts

4 → 12

Calls

4 calls:

712.0ms	(* (/ 1 (* 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
71.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
133.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
145.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify976.0ms

Counts: 135 → 135

prune666.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.6b

localize52.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.3b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
19.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
59.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
122.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts: 70 → 70

prune821.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 20.6b

regimes271.0ms

Accuracy

-1.9% (3.0b remaining)

Error of 26.0b against oracle of 23.0b and baseline of 26.0b

bsearch0.0ms

simplify35.0ms

end0.0ms

sample961.0ms

Algorithm

intervals

Results

574.0ms

8495×

body

valid