Details

sample53.0ms

Algorithm

intervals

Results

19.0ms	210×	body	80	nan
17.0ms	256×	body	80	valid

simplify6.0ms

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: 30.0b

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))
27.8b	(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:

14.0ms	(/ (+ (* (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)))

series391.0ms

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)))
95.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
154.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (47.0ms)

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

prune483.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)
16.0ms	(/ (+ (* (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))

series419.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot re im)
109.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
103.0ms	(* (log (* 1 (hypot re im))) (log base))
154.0ms	(* (log base) (log base))

simplify55.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

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

prune441.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize27.0ms

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

rewrite24.0ms

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:

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

420.0ms	(/ (/ (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))))
347.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
136.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
290.0ms	(* (log base) (log base))

simplify66.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	552	2653
1	2004	2343
2	5002	2317

prune583.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

2.0ms	(/ 1 (hypot (log base) 0.0))
14.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
2.0ms	(/ (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:

356.0ms	(/ 1 (hypot (log base) 0.0))
357.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
141.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
350.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	438	1833
1	2096	1608
2	5003	1588

prune436.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes229.0ms

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	17
1	26	17
2	26	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

552.0ms	8030×	body	80	nan
536.0ms	8000×	body	80	valid