Details

sample59.0ms

Algorithm

intervals

Results

23.0ms	283×	body	80	nan
18.0ms	256×	body	80	valid

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

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))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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:

13.0ms	(/ (+ (* (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))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
151.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

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

prune465.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
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))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`pow1`
22×	`add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac` `associate-l` `log-pow`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `associate-/l`
2×	`flip3-+` `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 → 110

Calls

4 calls:

0.0ms	(hypot re im)
15.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (log (* 1 (hypot re im))) (log base))
5.0ms	(* (log base) (log base))

series413.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot re im)
107.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
102.0ms	(* (log (* 1 (hypot re im))) (log base))
154.0ms	(* (log base) (log base))

simplify54.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	398	1152
1	1604	1012
2	5002	969

prune439.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

3.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
10.0ms	(/ (/ (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))
5.0ms	(* (log base) (log base))

series1.2s

Counts

4 → 12

Calls

4 calls:

337.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
567.0ms	(/ (/ (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))))
140.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
151.0ms	(* (log base) (log base))

simplify63.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	552	2655
1	2009	2343
2	5001	2317

prune579.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (log (exp (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))
5.7b	(exp (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 212

Calls

4 calls:

24.0ms	(/ (log (exp (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
4.0ms	(* (log base) (log base))
4.0ms	(exp (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

421.0ms	(/ (log (exp (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
140.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
153.0ms	(* (log base) (log base))
442.0ms	(exp (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	615	4932
1	2069	3974
2	5001	3878

prune735.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes253.0ms

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	21	18
1	21	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

573.0ms	8095×	body	80	nan
564.0ms	8000×	body	80	valid