Details

sample64.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
22.0ms	252×	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: 33.1b

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)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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))
8.0ms	(sqrt (+ (* re re) (* im im)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
94.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (49.0ms)

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

prune460.0ms

Filtered

131 candidates to 95 candidates (72.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Merged error: 0.2b

Counts

132 → 10

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 99

Calls

3 calls:

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))

series368.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
102.0ms	(* (log (hypot re im)) (log base))
152.0ms	(* (log base) (log base))

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	377	1035
1	1559	925
2	5002	895

prune356.0ms

Filtered

108 candidates to 73 candidates (67.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	94	14	108
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	104	14	118

Merged error: 0.0b

Counts

118 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot (log base) 0.0) 1))
0.4b	(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))
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)))

rewrite40.0ms

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))
18.0ms	(* (/ 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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

347.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
106.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
152.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
483.0ms	(* (/ 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)))

simplify96.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	940	3390
1	4243	2753
2	5002	2552

prune604.0ms

Filtered

248 candidates to 134 candidates (54.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	243	5	248
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	250	12	262

Merged error: 0b

Counts

262 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) 4))) 2) (- (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
21×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
17×	`add-cube-cbrt`
12×	`associate--l+`
8×	`associate-r` `prod-exp` `cbrt-unprod`
7×	`log-pow`
6×	`swap-sqr`
5×	`associate-l`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`frac-times` `sub-neg` `flip3--` `associate-r/` `prod-diff` `-commutative` `flip--`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `pow-exp` `pow-sqr` `pow-prod-up` `fma-udef` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

17.0ms	(* (* (/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) 4))) 2) (- (* (log base) (log base)) (* 0.0 0.0)))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(* (log base) (log base))
3.0ms	(pow (log base) 4)

series605.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (* (/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) 4))) 2) (- (* (log base) (log base)) (* 0.0 0.0)))
107.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
149.0ms	(* (log base) (log base))
169.0ms	(pow (log base) 4)

simplify106.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	629	1868
1	3444	1611
2	5001	1607

prune411.0ms

Filtered

128 candidates to 77 candidates (60.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	128	12	140

Merged error: 0b

Counts

140 → 12

regimes266.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	20
1	27	20

end0.0ms

sample1.9s

Algorithm

intervals

Results

761.0ms	8000×	body	80	valid
746.0ms	8227×	body	80	nan