Details

sample53.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	260×	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: 31.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.6b	(* (log base) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
103.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
156.0ms	(* (log base) (log base))
37.0ms	(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

prune464.0ms

Filtered

131 candidates to 95 candidates (72.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 0.2b

Counts

132 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.4b	(* (log (hypot re im)) (log base))
0.4b	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.6b	(* (log base) (log base))

rewrite21.0ms

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

series426.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot re im)
104.0ms	(* (log (hypot re im)) (log base))
114.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
157.0ms	(* (log base) (log base))

simplify54.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (43.0ms)

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

prune398.0ms

Filtered

121 candidates to 85 candidates (70.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	108	13	121
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 0b

Counts

132 → 13

localize21.0ms

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))
0.4b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
0.6b	(* (log base) (log base))

rewrite25.0ms

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))))
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))
5.0ms	(* (log base) (log base))

series769.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (/ (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))))
111.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
299.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
161.0ms	(* (log base) (log base))

simplify65.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	526	2615
1	1893	2303
2	5001	2279

prune531.0ms

Filtered

161 candidates to 110 candidates (68.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	5	161
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Merged error: 0b

Counts

174 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
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)) (fma 0.0 0.0 (pow (log base) 2)))
0.6b	(pow (log base) 2)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `pow-to-exp` `hypot-udef` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `log-pow` `fma-udef` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

1.0ms	(hypot re im)
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
3.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))
2.0ms	(pow (log base) 2)

series455.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
109.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
150.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))
150.0ms	(pow (log base) 2)

simplify107.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	231	703
1	675	626
2	3194	619
3	5003	615

prune260.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	82	11	93

Merged error: 0b

Counts

93 → 11

regimes252.0ms

Accuracy

0% (0.4b 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	15	10
1	15	10

end0.0ms

sample1.5s

Algorithm

intervals

Results

588.0ms	8000×	body	80	valid
552.0ms	7984×	body	80	nan