Details

sample49.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
14.0ms	220×	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

prune4.0ms

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: 30.4b

Counts

2 → 1

localize23.0ms

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

rewrite28.0ms

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)))

series376.0ms

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)))
91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
152.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (49.0ms)

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

prune477.0ms

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

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`pow1`
21×	`add-cube-cbrt`
12×	`log-prod`
9×	`add-exp-log` `times-frac` `associate-l` `log-pow` `add-cbrt-cube`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`flip3-+` `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`

Counts

3 → 100

Calls

3 calls:

10.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (* 1 (hypot re im))) (log base))
8.0ms	(* (log base) (log base))

series361.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
100.0ms	(* (log (* 1 (hypot re im))) (log base))
153.0ms	(* (log base) (log base))

simplify56.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	381	1125
1	1567	988
2	5001	945

prune532.0ms

Filtered

109 candidates to 76 candidates (69.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	13	109
Fresh	11	0	11
Picked	1	0	1
Done	0	0	0
Total	108	13	121

Merged error: 0.0b

Counts

121 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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))
18.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
4.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
1.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

347.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
364.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
343.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
139.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	936	3396
1	4367	2773
2	5001	2572

prune628.0ms

Filtered

248 candidates to 134 candidates (54.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	243	5	248
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	250	11	261

Merged error: 0b

Counts

261 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
0.3b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (* 1 (hypot re im))) (log base))
0.5b	(* (log base) (log base))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 186

Calls

4 calls:

11.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
10.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(* (log (* 1 (hypot re im))) (log base))
5.0ms	(* (log base) (log base))

series514.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
144.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
96.0ms	(* (log (* 1 (hypot re im))) (log base))
145.0ms	(* (log base) (log base))

simplify99.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	662	3288
1	3099	2903
2	5001	2776

prune638.0ms

Filtered

198 candidates to 124 candidates (62.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	199	10	209

Merged error: 0b

Counts

209 → 10

regimes224.0ms

Accuracy

0% (0.5b 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	20	13
1	20	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

535.0ms	8000×	body	80	valid
507.0ms	8005×	body	80	nan