Details

sample54.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
15.0ms	228×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite76.0ms

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))
37.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
13.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
105.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
151.0ms	(* (log base) (log base))
40.0ms	(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

prune491.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (log (hypot re im)))) (log base))
0.3b	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
5.8b	(exp (log (hypot re im)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`pow1`
15×	`log-prod`
14×	`log-pow`
12×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`exp-prod` `associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum` `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` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `rem-exp-log`

Counts

4 → 120

Calls

4 calls:

19.0ms	(* (log (exp (log (hypot re im)))) (log base))
40.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
3.0ms	(exp (log (hypot re im)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (log (exp (log (hypot re im)))) (log base))
117.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
155.0ms	(* (log base) (log base))
50.0ms	(exp (log (hypot re im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	422	1267
1	1601	1092
2	5001	1044

prune501.0ms

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))
0.3b	(/ (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))))
0.5b	(* (log base) (log base))

rewrite50.0ms

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:

0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
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))))
13.0ms	(* (log base) (log base))

series1.1s

Counts

4 → 12

Calls

4 calls:

149.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
358.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
446.0ms	(/ (/ (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))))
153.0ms	(* (log base) (log base))

simplify63.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (43.0ms)

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

prune622.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))
0.3b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.3b	(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
0.5b	(pow (log base) 2)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-to-exp` `pow-flip` `pow-pow` `pow-exp` `associate-/r/` `log-pow` `fma-udef` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

10.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
5.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
3.0ms	(pow (log base) 2)

series1.2s

Counts

4 → 12

Calls

4 calls:

320.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))
147.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
391.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
302.0ms	(pow (log base) 2)

simplify61.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	466	2240
1	2031	1988
2	5001	1912

prune450.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes282.0ms

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	26	17
1	28	17
2	28	17

end0.0ms

sample1.6s

Algorithm

intervals

Results

561.0ms	8062×	body	80	nan
542.0ms	8000×	body	80	valid