Details

sample54.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
14.0ms	217×	body	80	nan

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	33	16
2	33	16
done	33	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `hypot-def` `div-inv`

Counts

4 → 119

Calls

4 calls:

39.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
96.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
146.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	467	1408
1	1820	1268
2	5001	1217
done	5001	1217

prune480.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (* 1 (hypot re im))) (log base))
0.5b	(* (log base) (log base))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`pow1`
21×	`add-cube-cbrt`
12×	`log-prod`
9×	`add-exp-log` `times-frac` `associate-l` `log-pow` `add-cbrt-cube`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`flip3-+` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

3 → 100

Calls

3 calls:

40.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (log (* 1 (hypot re im))) (log base))
10.0ms	(* (log base) (log base))

series366.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
105.0ms	(* (log (* 1 (hypot re im))) (log base))
149.0ms	(* (log base) (log base))

simplify57.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	381	1125
1	1567	988
2	5001	945
done	5001	945

prune392.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.4b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
0.5b	(* (log base) (log base))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
44×	`add-sqr-sqrt` `*-un-lft-identity`
42×	`add-cube-cbrt`
25×	`add-exp-log`
24×	`sqrt-prod`
20×	`add-cbrt-cube`
17×	`pow1`
10×	`div-exp` `associate-/l*`
9×	`div-inv`
7×	`cbrt-undiv` `associate-/r*`
6×	`log-prod` `swap-sqr` `log-pow`
5×	`prod-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod`
2×	`frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/r/`
1×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

26.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
8.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
10.0ms	(* (log base) (log base))

series1.2s

Counts

4 → 12

Calls

4 calls:

572.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
147.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
351.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
150.0ms	(* (log base) (log base))

simplify63.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	552	2655
1	2004	2343
2	5002	2317
done	5002	2317

prune597.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
0.4b	(* (log (* 1 (hypot re im))) (log base))
0.4b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(* (log base) (log base))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
70×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
66×	`add-cube-cbrt`
24×	`pow1`
21×	`add-exp-log`
18×	`associate-/r*`
15×	`add-cbrt-cube`
12×	`log-prod`
11×	`associate-/r/`
9×	`associate-l` `log-pow`
8×	`div-exp` `associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `swap-sqr` `flip-+` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`rec-exp` `frac-2neg` `1-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow2` `pow-flip` `pow-plus` `pow-sqr` `pow-prod-up` `inv-pow`

Counts

4 → 186

Calls

4 calls:

28.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
18.0ms	(* (log (* 1 (hypot re im))) (log base))
38.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
10.0ms	(* (log base) (log base))

series540.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
103.0ms	(* (log (* 1 (hypot re im))) (log base))
154.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
146.0ms	(* (log base) (log base))

simplify96.0ms

Counts

198 → 198

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	662	3288
1	3099	2903
2	5001	2776
done	5001	2776

prune541.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes217.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	15
1	27	15
2	27	15
done	27	15

end0.0ms

sample1.5s

Algorithm

intervals

Results

525.0ms	8000×	body	80	valid
518.0ms	7931×	body	80	nan