Details

sample117.0ms

Algorithm

intervals

Results

42.0ms	314×	body	80	nan
33.0ms	256×	body	80	valid

simplify81.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	74
3	56
2	44
1	27
0	18

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize52.0ms

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)))
0.3b	(* (atan2 im re) (log base))
0.6b	(* (log base) (log base))
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-cbrt-cube` `add-exp-log`
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-+` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `div-sub` `div-exp` `pow-sqr` `pow-prod-up` `div-inv` `flip--`

Counts

4 → 108

Calls

4 calls:

39.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
7.0ms	(* (atan2 im re) (log base))
9.0ms	(* (log base) (log base))
13.0ms	(sqrt (+ (* re re) (* im im)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
37.0ms	(* (atan2 im re) (log base))
288.0ms	(* (log base) (log base))
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	2938
1	508
0	194

prune882.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (+ 0 (log base)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
15×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`distribute-lft-out`
5×	`pow1` `associate-/r*`
4×	`log-pow`
3×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 37

Calls

1 calls:

20.0ms

(/ (atan2 im re) (+ 0 (log base)))

series64.0ms

Counts

1 → 3

Calls

1 calls:

64.0ms

(/ (atan2 im re) (+ 0 (log base)))

simplify337.0ms

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
2	653
1	157
0	74

prune304.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 74

Calls

2 calls:

14.0ms	(* (atan2 im re) (/ 1 (log base)))
7.0ms	(/ 1 (log base))

series322.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(* (atan2 im re) (/ 1 (log base)))
269.0ms	(/ 1 (log base))

simplify3.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	2031
1	222
0	100

prune299.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (atan2 im re) (- (* (log base) (log base))))
0.3b	(* (/ (atan2 im re) (- (* (log base) (log base)))) (- 0 (log base)))
0.6b	(* (log base) (log base))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`times-frac`
36×	`*-un-lft-identity`
31×	`add-cube-cbrt`
26×	`associate-l`
19×	`pow1`
12×	`add-cbrt-cube` `add-exp-log`
10×	`associate-r`
7×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `log-pow`
6×	`log-prod` `associate-/r*` `swap-sqr`
5×	`distribute-rgt-in` `distribute-lft-in`
3×	`prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `sub-neg` `flip3--` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--` `distribute-lft-out--`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `associate-*l/` `pow-sqr` `pow-prod-up` `distribute-rgt-neg-out` `difference-of-squares` `sub0-neg`

Counts

3 → 128

Calls

3 calls:

5.0ms	(/ (atan2 im re) (- (* (log base) (log base))))
40.0ms	(* (/ (atan2 im re) (- (* (log base) (log base)))) (- 0 (log base)))
15.0ms	(* (log base) (log base))

series332.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(/ (atan2 im re) (- (* (log base) (log base))))
53.0ms	(* (/ (atan2 im re) (- (* (log base) (log base)))) (- 0 (log base)))
183.0ms	(* (log base) (log base))

simplify3.2s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	4803
1	542
0	201

prune769.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes463.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
1.6s	7990×	body	80	nan