Details

sample84.0ms

Algorithm

intervals

Results

31.0ms	314×	body	80	nan
24.0ms	256×	body	80	valid

simplify86.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	106
6	106
5	102
4	88
3	68
2	52
1	31
0	18

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (fma (- 0.0) (log (hypot im re)) (* (log base) (atan2 im re))) (fma (log base) (log base) (* 0.0 0.0)))
0.3b	(* (log base) (atan2 im re))
0.6b	(fma (log base) (log base) (* 0.0 0.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`associate-l`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `log1p-expm1-u` `associate-/l` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

4.0ms	(/ (fma (- 0.0) (log (hypot im re)) (* (log base) (atan2 im re))) (fma (log base) (log base) (* 0.0 0.0)))
6.0ms	(* (log base) (atan2 im re))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series628.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(/ (fma (- 0.0) (log (hypot im re)) (* (log base) (atan2 im re))) (fma (log base) (log base) (* 0.0 0.0)))
53.0ms	(* (log base) (atan2 im re))
389.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify493.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	727
1	222
0	116

prune667.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (hypot 0.0 (log base))) (/ (fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0))) (hypot 0.0 (log base))))
0.3b	(/ 1 (hypot 0.0 (log base)))
0.3b	(/ (fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0))) (hypot 0.0 (log base)))
0.3b	(fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

39.0ms	(* (/ 1 (hypot 0.0 (log base))) (/ (fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0))) (hypot 0.0 (log base))))
7.0ms	(/ 1 (hypot 0.0 (log base)))
7.0ms	(/ (fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0))) (hypot 0.0 (log base)))
1.0ms	(fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

329.0ms	(* (/ 1 (hypot 0.0 (log base))) (/ (fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0))) (hypot 0.0 (log base))))
977.0ms	(/ 1 (hypot 0.0 (log base)))
242.0ms	(/ (fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0))) (hypot 0.0 (log base)))
75.0ms	(fma (log base) (atan2 im re) (* (log (hypot im re)) (- 0.0)))

simplify1.8s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	3066
1	469
0	182

prune960.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
1×	`expm1-log1p-u` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

7.0ms

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

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify911.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
3	1366
2	302
1	110
0	64

prune261.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.3b

(/ (fma (log base) (atan2 im re) (* (- (log (hypot im re))) 0.0)) (* (hypot 0.0 (log base)) (hypot 0.0 (log base))))

0.3b

(fma (log base) (atan2 im re) (* (- (log (hypot im re))) 0.0))

0.6b

(* (hypot 0.0 (log base)) (hypot 0.0 (log base)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
4×	`hypot-udef`
3×	`expm1-log1p-u` `times-frac` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `clear-num` `associate-/r` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `fma-udef` `div-inv` `unswap-sqr`

Counts

3 → 62

Calls

3 calls:

12.0ms

(/ (fma (log base) (atan2 im re) (* (- (log (hypot im re))) 0.0)) (* (hypot 0.0 (log base)) (hypot 0.0 (log base))))

0.0ms

(fma (log base) (atan2 im re) (* (- (log (hypot im re))) 0.0))

9.0ms

(* (hypot 0.0 (log base)) (hypot 0.0 (log base)))

series970.0ms

Counts

3 → 9

Calls

3 calls:

350.0ms

(/ (fma (log base) (atan2 im re) (* (- (log (hypot im re))) 0.0)) (* (hypot 0.0 (log base)) (hypot 0.0 (log base))))

122.0ms

(fma (log base) (atan2 im re) (* (- (log (hypot im re))) 0.0))

498.0ms

(* (hypot 0.0 (log base)) (hypot 0.0 (log base)))

simplify953.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1135
1	258
0	103

prune496.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes389.0ms

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	6
0	6

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.6s	7990×	body	80	nan