Details

sample59.0ms

Algorithm

intervals

Results

19.0ms	289×	body	80	nan
17.0ms	256×	body	80	valid

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: 35.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite79.0ms

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:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
40.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
102.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

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

prune455.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

0.0ms	(hypot re im)
10.0ms	(* (log (hypot re im)) (log base))
38.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
11.0ms	(* (log base) (log base))

series419.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
102.0ms	(* (log (hypot re im)) (log base))
113.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
153.0ms	(* (log base) (log base))

simplify52.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	394	1062
1	1578	949
2	5001	919
done	5001	919

prune389.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
70×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
66×	`add-cube-cbrt`
22×	`pow1`
21×	`add-exp-log`
18×	`associate-/r*`
15×	`add-cbrt-cube`
12×	`log-prod`
11×	`associate-/r/`
8×	`div-exp` `associate-r` `associate-l` `log-pow`
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`
2×	`rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `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 → 185

Calls

4 calls:

28.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0))))
10.0ms	(* (log (hypot re im)) (log base))
34.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)))
10.0ms	(* (log base) (log base))

series682.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0))))
99.0ms	(* (log (hypot re im)) (log base))
147.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)))
301.0ms	(* (log base) (log base))

simplify90.0ms

Counts

197 → 197

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	658	3059
1	3095	2734
2	5001	2624
done	5001	2624

prune538.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base))) (* (* (atan2 im re) 0.0) (* (atan2 im re) 0.0))) (* (- (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0))))
0.4b	(* (- (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.5b	(* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base)))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
23×	`add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down`
14×	`add-sqr-sqrt`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`add-cube-cbrt` `log-prod` `*-un-lft-identity`
10×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-l/` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`flip3--` `flip--` `fma-udef`
2×	`cbrt-undiv` `pow-plus` `div-exp` `associate-/r/` `*-commutative` `associate-/l/` `difference-of-squares`
1×	`pow2` `frac-2neg` `div-sub` `swap-sqr` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

96.0ms	(/ (- (* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base))) (* (* (atan2 im re) 0.0) (* (atan2 im re) 0.0))) (* (- (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0))))
29.0ms	(* (- (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
33.0ms	(* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series694.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base))) (* (* (atan2 im re) 0.0) (* (atan2 im re) 0.0))) (* (- (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0))))
147.0ms	(* (- (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
129.0ms	(* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base)))
272.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify86.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	575	2109
1	2871	1764
2	5001	1756
done	5001	1756

prune371.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes204.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	38
1	29	38
done	29	38

end0.0ms

sample1.6s

Algorithm

intervals

Results

563.0ms	8043×	body	80	nan
547.0ms	8000×	body	80	valid