Details

sample59.0ms

Algorithm

intervals

Results

20.0ms	292×	body	80	nan
17.0ms	256×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 29.9b

localize23.0ms

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))
0.4b	(* (log base) (log base))
27.7b	(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)))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
81.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
143.0ms	(* (log base) (log base))
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (47.0ms)

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

prune456.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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))
0.4b	(* (log base) (log base))

rewrite74.0ms

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)
42.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
19.0ms	(* (log (* 1 (hypot re im))) (log base))
10.0ms	(* (log base) (log base))

series373.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(hypot re im)
101.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
92.0ms	(* (log (* 1 (hypot re im))) (log base))
141.0ms	(* (log base) (log base))

simplify60.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune421.0ms

Pruning

12 alts after pruning (12 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))
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	(* (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:

8.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
23.0ms	(/ (/ (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))
10.0ms	(* (log base) (log base))

series979.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
383.0ms	(/ (/ (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))))
135.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
141.0ms	(* (log base) (log base))

simplify69.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	552	2653
1	2009	2343
2	5001	2317

prune570.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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:

23.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
5.0ms	(/ 1 (hypot (log base) 0.0))
8.0ms	(/ (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))

series1.1s

Counts

4 → 12

Calls

4 calls:

338.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
335.0ms	(/ 1 (hypot (log base) 0.0))
331.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
130.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	438	1833
1	2075	1608
2	5001	1578

prune444.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes237.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

560.0ms	8023×	body	80	nan
541.0ms	8000×	body	80	valid