Details

sample74.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
27.0ms	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize23.0ms

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))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
100.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (47.0ms)

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

prune485.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(* (log (hypot re im)) (log base))
0.3b	(/ (+ (* (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))

rewrite24.0ms

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:

0.0ms	(hypot re im)
4.0ms	(* (log (hypot re im)) (log base))
12.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))

series412.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
101.0ms	(* (log (hypot re im)) (log base))
108.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms	(* (log base) (log base))

simplify51.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (41.0ms)

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

prune398.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

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

series605.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
106.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
193.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
150.0ms	(* (log base) (log base))

simplify61.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	526	2615
1	1898	2303
2	5001	2279

prune704.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
46×	`add-cube-cbrt`
27×	`add-exp-log`
24×	`sqrt-prod`
22×	`add-cbrt-cube`
21×	`pow1`
12×	`log-prod`
10×	`div-exp` `associate-/l*`
9×	`div-inv`
8×	`associate-r` `associate-l` `log-pow`
7×	`cbrt-undiv` `associate-/r*`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `flip3-+` `sqrt-div` `1-exp` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `flip-+` `unswap-sqr`
1×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 169

Calls

4 calls:

18.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
8.0ms	(* (log (hypot re im)) (log base))
29.0ms	(/ (/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
4.0ms	(* (log base) (log base))

series535.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
101.0ms	(* (log (hypot re im)) (log base))
153.0ms	(/ (/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
144.0ms	(* (log base) (log base))

simplify75.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	633	2867
1	2484	2530
2	5001	2508

prune528.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes239.0ms

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	27	18
1	29	18
2	29	18

end0.0ms

sample2.1s

Algorithm

intervals

Results

915.0ms	8000×	body	80	valid
766.0ms	7750×	body	80	nan