Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
18.0ms	266×	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

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: 31.9b

Counts

2 → 1

localize18.0ms

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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

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)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
88.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
146.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (47.0ms)

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

prune447.0ms

Filtered

131 candidates to 95 candidates (72.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	122	9	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	9	132

Merged error: 0.1b

Counts

132 → 9

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))

series350.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(/ (+ (* (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))

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (42.0ms)

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

prune347.0ms

Filtered

108 candidates to 73 candidates (67.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	107	10	117

Merged error: 0b

Counts

117 → 10

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

rewrite27.0ms

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:

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))))
7.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(* (log base) (log base))

series678.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(/ (/ (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))))
165.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
123.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
159.0ms	(* (log base) (log base))

simplify65.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	526	2617
1	1893	2303
2	5001	2279

prune682.0ms

Filtered

161 candidates to 110 candidates (68.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	162	9	171

Merged error: 0b

Counts

171 → 9

localize28.0ms

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)))
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)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity`
54×	`add-cube-cbrt`
19×	`pow1`
13×	`associate-/l*`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`log-pow`
6×	`log-prod` `swap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `unpow-prod-down` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `pow-unpow` `distribute-lft-in` `div-exp` `associate-/r*`
1×	`pow2` `pow-to-exp` `pow-pow` `frac-2neg` `pow-plus` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `associate-/l/` `unswap-sqr` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

6.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) 4)))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)

series574.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) 4)))
100.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
141.0ms	(* (log base) (log base))
159.0ms	(pow (log base) 4)

simplify72.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	563	2070
1	2404	1940
2	5001	1936

prune652.0ms

Filtered

152 candidates to 112 candidates (73.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	152	9	161

Merged error: 0b

Counts

161 → 9

regimes199.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	17
1	26	17
2	26	17

end0.0ms

sample1.5s

Algorithm

intervals

Results

578.0ms	8000×	body	80	valid
543.0ms	8146×	body	80	nan