Details

sample29.0ms

Algorithm

intervals

Results

13.0ms

274×

body

valid

simplify68.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize33.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
27.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

9.0ms	(- (* x.im y.re) (* x.re y.im))
53.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series212.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (* x.im y.re) (* x.re y.im))
153.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts: 50 → 50

prune196.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.9b

localize22.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
16.3b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite89.0ms

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:

15.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
22.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* x.im y.re) (* x.re y.im))
191.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts: 98 → 98

prune492.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.9b

localize34.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
16.4b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

9.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
25.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* x.im y.re) (* x.re y.im))
144.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
72.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts: 97 → 97

prune439.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 24.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.6b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
1.1b	(- (* x.im y.re) (* x.re y.im))
26.8b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

24.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(- (* x.im y.re) (* x.re y.im))
83.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series259.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
53.0ms	(- (* x.im y.re) (* x.re y.im))
131.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify792.0ms

Counts: 96 → 96

prune248.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.9b

regimes318.0ms

Accuracy

-2.6% (3.0b remaining)

Error of 26.4b against oracle of 23.4b and baseline of 26.4b

bsearch2.0ms

simplify349.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8468×

body

valid