Details

sample80.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
28.0ms	216×	body	80	nan

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

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)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
30.0b	(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:

13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
8.0ms	(* (log base) (log base))
6.0ms	(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

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

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)))
0.3b	(* (log (hypot re im)) (log base))
0.5b	(* (log base) (log base))

rewrite23.0ms

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)
11.0ms	(/ (+ (* (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))
4.0ms	(* (log base) (log base))

series66.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(hypot re im)
26.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
22.0ms	(* (log (hypot re im)) (log base))
10.0ms	(* (log base) (log base))

simplify52.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (42.0ms)

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

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
157×	`times-frac`
104×	`add-sqr-sqrt`
93×	`div-exp`
90×	`*-un-lft-identity`
85×	`add-cube-cbrt`
62×	`prod-exp`
50×	`add-cbrt-cube`
44×	`associate-l`
41×	`1-exp`
20×	`cbrt-undiv`
15×	`rec-exp`
14×	`associate-/r*`
13×	`cbrt-unprod`
11×	`div-inv`
7×	`pow1` `associate-r` `unswap-sqr`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 236

Calls

4 calls:

5.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
30.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
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))

series178.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
81.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
44.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
25.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	940	3378
1	4364	2753
2	5001	2552

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (expm1 (log1p (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.3b	(* (log (expm1 (log1p (hypot re im)))) (log base))
0.5b	(* (log base) (log base))
4.7b	(expm1 (log1p (hypot re im)))

rewrite23.0ms

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` `expm1-log1p` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `expm1-udef`

Counts

4 → 110

Calls

4 calls:

12.0ms	(/ (+ (* (log (expm1 (log1p (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log (expm1 (log1p (hypot re im)))) (log base))
5.0ms	(* (log base) (log base))
0.0ms	(expm1 (log1p (hypot re im)))

series137.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (+ (* (log (expm1 (log1p (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
54.0ms	(* (log (expm1 (log1p (hypot re im)))) (log base))
8.0ms	(* (log base) (log base))
20.0ms	(expm1 (log1p (hypot re im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	592	1466
1	2542	1328
2	5001	1301

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes591.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15

end0.0ms

sample2.3s

Algorithm

intervals

Results

963.0ms	8129×	body	80	nan
951.0ms	8000×	body	80	valid