Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
16.0ms	253×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize19.0ms

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))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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:

10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

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

prune469.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`pow1`
12×	`log-prod`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-r` `associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`flip3-+` `pow-prod-down` `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 → 99

Calls

3 calls:

9.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (log (hypot re im)) (log base))
5.0ms	(* (log base) (log base))

series353.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
100.0ms	(* (log (hypot re im)) (log base))
147.0ms	(* (log base) (log base))

simplify51.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	377	1035
1	1559	925
2	5002	895

prune368.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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:

11.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
4.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(* (log base) (log base))

series589.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
146.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
104.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
148.0ms	(* (log base) (log base))

simplify198.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	526	2617
1	1893	2303
2	5001	2279

prune576.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

735×	`times-frac`
355×	`add-sqr-sqrt` `*-un-lft-identity`
353×	`add-cube-cbrt`
135×	`sqrt-prod`
47×	`associate-/l*`
30×	`div-inv`
27×	`add-exp-log`
17×	`pow1` `add-cbrt-cube`
15×	`div-exp`
9×	`associate-/r*` `associate-/r/`
7×	`cbrt-undiv`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num`
1×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 416

Calls

4 calls:

19.0ms	(/ (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
3.0ms	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(* (log base) (log base))

series1.0s

Counts

4 → 12

Calls

4 calls:

416.0ms	(/ (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
374.0ms	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
108.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
143.0ms	(* (log base) (log base))

simplify121.0ms

Algorithm

egg-herbie

Counts

428 → 428

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1572	11552
1	5001	9657

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes235.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

537.0ms	8000×	body	80	valid
520.0ms	8212×	body	80	nan