Details

sample76.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
23.0ms	239×	body	80	nan

simplify5.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (atan2 im re) (log base))
0.4b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 108

Calls

4 calls:

9.0ms	(* (atan2 im re) (log base))
32.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
27.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 im re) (log base))
43.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
175.0ms	(* (log base) (log base))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Counts: 120 → 120

prune475.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (/ 1 base))
0.3b	(/ (atan2 im re) (log (/ 1 base)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`log-pow`
13×	`log-prod`
12×	`pow1`
9×	`add-exp-log`
6×	`associate-/r*`
5×	`pow-flip` `inv-pow`
4×	`rem-log-exp` `add-cbrt-cube`
3×	`div-exp` `associate-/l*`
2×	`div-inv` `add-log-exp`
1×	`cbrt-undiv` `log-div` `rec-exp` `frac-2neg` `1-exp` `log-rec` `clear-num`

Counts

2 → 68

Calls

2 calls:

4.0ms	(log (/ 1 base))
9.0ms	(/ (atan2 im re) (log (/ 1 base)))

series187.0ms

Counts

2 → 6

Calls

2 calls:

148.0ms	(log (/ 1 base))
39.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify96.0ms

Counts: 74 → 74

prune186.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ -1 (log base))
0.3b	(* (atan2 im re) (/ -1 (log base)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 66

Calls

2 calls:

6.0ms	(/ -1 (log base))
16.0ms	(* (atan2 im re) (/ -1 (log base)))

series255.0ms

Counts

2 → 6

Calls

2 calls:

199.0ms	(/ -1 (log base))
56.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify34.0ms

Counts: 72 → 72

prune184.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
0.3b	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

34×	`log-prod`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
22×	`associate-+r+`
21×	`cbrt-prod`
12×	`associate-+l+`
10×	`distribute-rgt-out` `log-pow`
9×	`pow1`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
5×	`pow-flip` `associate-/r*` `inv-pow` `add-log-exp`
3×	`log-rec` `associate-/l*`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+` `div-inv`
1×	`cbrt-undiv` `+-commutative` `distribute-lft-neg-out` `associate-+r-` `log-div` `distribute-neg-out` `frac-2neg` `div-exp` `unsub-neg` `clear-num` `sum-log`

Counts

4 → 110

Calls

4 calls:

19.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
25.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.3s

Counts

4 → 12

Calls

4 calls:

639.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
247.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
207.0ms	(cbrt base)
216.0ms	(cbrt base)

simplify41.0ms

Counts: 122 → 122

prune492.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes188.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	8219×	body	80	nan
1.2s	8000×	body	80	valid