Details

sample50.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
14.0ms	216×	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

prune7.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 34.1b

Counts

2 → 1

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))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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:

10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
150.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (50.0ms)

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

prune454.0ms

Filtered

131 candidates to 95 candidates (72.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Merged error: 0.2b

Counts

132 → 12

localize20.0ms

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))

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)))
5.0ms	(* (log (hypot re im)) (log base))
5.0ms	(* (log base) (log base))

series399.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot re im)
105.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
97.0ms	(* (log (hypot re im)) (log base))
148.0ms	(* (log base) (log base))

simplify55.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (44.0ms)

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

prune519.0ms

Filtered

121 candidates to 85 candidates (70.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	11	0	11
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Merged error: 0b

Counts

133 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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:

6.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
4.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
17.0ms	(* (/ 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)))

series945.0ms

Counts

4 → 12

Calls

4 calls:

347.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
102.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
151.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
344.0ms	(* (/ 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)))

simplify95.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	940	3378
1	4369	2753
2	5001	2552

prune649.0ms

Filtered

248 candidates to 134 candidates (54.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	246	2	248
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	248	10	258

Merged error: 0b

Counts

258 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log base) (* 2 (log (cbrt base))))
0.3b	(* (log (hypot re im)) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

7.0ms	(* (log base) (* 2 (log (cbrt base))))
5.0ms	(* (log (hypot re im)) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series839.0ms

Counts

4 → 12

Calls

4 calls:

396.0ms	(* (log base) (* 2 (log (cbrt base))))
100.0ms	(* (log (hypot re im)) (log base))
170.0ms	(cbrt base)
172.0ms	(cbrt base)

simplify134.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	350	747
1	1065	660
2	4495	627
3	5001	627

prune348.0ms

Filtered

111 candidates to 72 candidates (64.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	111	10	121

Merged error: 0b

Counts

121 → 10

regimes233.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	15
1	24	15
2	24	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

537.0ms	8000×	body	80	valid
502.0ms	7762×	body	80	nan