Details

sample91.0ms

Algorithm

intervals

Results

32.0ms	281×	body	80	nan
28.0ms	256×	body	80	valid

simplify68.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.6b	(* (log base) (log base))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

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:

40.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
11.0ms	(* (atan2 im re) (log base))
11.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
42.0ms	(* (atan2 im re) (log base))
190.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify861.0ms

Counts: 120 → 120

prune667.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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:

5.0ms	(log (/ 1 base))
11.0ms	(/ (atan2 im re) (log (/ 1 base)))

series233.0ms

Counts

2 → 6

Calls

2 calls:

174.0ms	(log (/ 1 base))
59.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify1.6s

Counts: 74 → 74

prune218.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

65×	`cbrt-prod`
63×	`times-frac`
58×	`*-un-lft-identity`
53×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`log-prod`
32×	`associate-+l+`
16×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
10×	`distribute-rgt-out`
9×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `div-inv`
5×	`distribute-lft1-in` `log-pow` `add-log-exp`
3×	`cbrt-div` `associate-/l*`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `log-div` `frac-2neg` `div-exp` `clear-num` `sum-log`

Counts

4 → 148

Calls

4 calls:

34.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
27.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
4.0ms	(cbrt (/ 1 base))
4.0ms	(cbrt (/ 1 base))

series991.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
123.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
256.0ms	(cbrt (/ 1 base))
266.0ms	(cbrt (/ 1 base))

simplify1.2s

Counts: 160 → 160

prune695.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* 2 (log (pow base -1/3))) (log (cbrt (/ 1 base))))
0.3b	(/ (atan2 im re) (+ (* 2 (log (pow base -1/3))) (log (cbrt (/ 1 base)))))
0.6b	(cbrt (/ 1 base))
5.0b	(pow base -1/3)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
30×	`log-prod`
27×	`times-frac`
26×	`cbrt-prod`
16×	`associate-+r+`
14×	`associate-+l+`
9×	`unpow-prod-down`
7×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
6×	`add-cbrt-cube`
5×	`pow1` `add-log-exp`
3×	`pow-unpow` `associate-/r` `div-inv` `associate-/l` `sqr-pow`
2×	`cbrt-div` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `log-div` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log`

Counts

4 → 110

Calls

4 calls:

29.0ms	(+ (* 2 (log (pow base -1/3))) (log (cbrt (/ 1 base))))
18.0ms	(/ (atan2 im re) (+ (* 2 (log (pow base -1/3))) (log (cbrt (/ 1 base)))))
4.0ms	(cbrt (/ 1 base))
4.0ms	(pow base -1/3)

series1.4s

Counts

4 → 12

Calls

4 calls:

677.0ms	(+ (* 2 (log (pow base -1/3))) (log (cbrt (/ 1 base))))
207.0ms	(/ (atan2 im re) (+ (* 2 (log (pow base -1/3))) (log (cbrt (/ 1 base)))))
263.0ms	(cbrt (/ 1 base))
224.0ms	(pow base -1/3)

simplify2.0s

Counts: 122 → 122

prune717.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.2s

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	8204×	body	80	nan
1.1s	8000×	body	80	valid