Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

274×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune2.0ms

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: 25.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
25.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 61

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series136.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
80.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify130.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462

prune193.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	8	71

Merged error: 15.8b

Counts

71 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.3b	(fma x.re y.re (* x.im y.im))
15.5b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

7.0ms	(/ 1 (* (hypot y.re y.im) 1))
11.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
1.0ms	(fma x.re y.re (* x.im y.im))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series375.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (* (hypot y.re y.im) 1))
176.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
36.0ms	(fma x.re y.re (* x.im y.im))
110.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify44.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884

prune264.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	148	9	157
Fresh	6	0	6
Picked	1	0	1
Done	0	1	1
Total	155	10	165

Merged error: 5.8b

Counts

165 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
15.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
23×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 99

Calls

4 calls:

1.0ms	(hypot y.re y.im)
9.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
1.0ms	(fma x.re y.re (* x.im y.im))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series346.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(hypot y.re y.im)
130.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
36.0ms	(fma x.re y.re (* x.im y.im))
109.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify96.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	308	794
1	1149	701
2	3275	701
3	5001	693

prune305.0ms

Filtered

111 candidates to 89 candidates (80.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	108	13	121

Merged error: 5.7b

Counts

121 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
0.3b	(fma x.re y.re (* x.im y.im))
0.5b	(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
15.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
41×	`add-exp-log`
40×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-cbrt-cube`
19×	`pow1`
18×	`sqrt-prod`
16×	`div-exp` `associate-/l*`
13×	`prod-exp`
10×	`cbrt-undiv`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
7×	`cbrt-unprod`
6×	`associate-r` `associate-l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `1-exp` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 146

Calls

4 calls:

12.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
1.0ms	(fma x.re y.re (* x.im y.im))
6.0ms	(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series314.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
39.0ms	(fma x.re y.re (* x.im y.im))
45.0ms	(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
115.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify71.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	454	1084
1	2499	890
2	5001	877

prune346.0ms

Filtered

158 candidates to 101 candidates (63.9%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	156	15	171

Merged error: 5.7b

Counts

171 → 15

regimes310.0ms

Accuracy

37.5% (7.0b remaining)

Error of 12.7b against oracle of 5.7b and baseline of 16.9b

bsearch61.0ms

Steps

Iters	Range		Point
7	3.110085981024015e+154	8.769655940674386e+155	3.997498131334168e+155
7	-1.8864815038392082e+94	-2.1159267475207395e+92	-7.863570656598141e+93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	30	14
2	30	14

end0.0ms

sample517.0ms

Algorithm

intervals

Results

305.0ms

8506×

body

valid