Details

sample55.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
17.0ms	265×	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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

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))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

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

prune489.0ms

Filtered

131 candidates to 95 candidates (72.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
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))

rewrite22.0ms

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:

1.0ms	(hypot re im)
9.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log (hypot re im)) (log base))
5.0ms	(* (log base) (log base))

series415.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot re im)
109.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
104.0ms	(* (log (hypot re im)) (log base))
152.0ms	(* (log base) (log base))

simplify53.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (43.0ms)

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

prune428.0ms

Filtered

121 candidates to 85 candidates (70.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
0.3b	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
0.4b	(* (log (hypot re im)) (log base))
0.5b	(pow (log base) 2)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

151×	`times-frac`
109×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
88×	`add-cube-cbrt`
48×	`add-exp-log` `associate-r`
24×	`div-exp`
20×	`add-cbrt-cube`
13×	`pow1` `associate-/r*`
12×	`1-exp`
11×	`prod-exp`
9×	`div-inv`
8×	`unswap-sqr`
7×	`associate-l`
6×	`cbrt-undiv` `rec-exp` `log-prod`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `log-pow` `associate-/l*`
2×	`frac-times` `flip3-+` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `flip-+`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `un-div-inv` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 214

Calls

4 calls:

6.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
18.0ms	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
5.0ms	(* (log (hypot re im)) (log base))
3.0ms	(pow (log base) 2)

series608.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
138.0ms	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
102.0ms	(* (log (hypot re im)) (log base))
154.0ms	(pow (log base) 2)

simplify102.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	817	2448
1	3803	2055
2	5001	1844

prune823.0ms

Filtered

226 candidates to 130 candidates (57.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (cbrt base)))
0.4b	(* (log base) (* 2 (log (cbrt base))))
0.5b	(cbrt base)
0.5b	(cbrt base)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
24×	`cbrt-prod`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`*-commutative`
1×	`unswap-sqr`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (log base) (log (cbrt base)))
7.0ms	(* (log base) (* 2 (log (cbrt base))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.2s

Counts

4 → 12

Calls

4 calls:

396.0ms	(* (log base) (log (cbrt base)))
415.0ms	(* (log base) (* 2 (log (cbrt base))))
178.0ms	(cbrt base)
174.0ms	(cbrt base)

simplify51.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	314	813
1	1256	728
2	5002	688

prune435.0ms

Filtered

118 candidates to 77 candidates (65.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes262.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	20
1	27	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

547.0ms	8000×	body	80	valid
540.0ms	8197×	body	80	nan