Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

273×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

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: 29.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.2b	(+ (* x.re y.re) (* x.im y.im))
28.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
84.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify137.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (33.0ms)

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

prune184.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 16.9b

Counts

71 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
16.5b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite27.0ms

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:

4.0ms	(/ 1 (* (hypot y.re y.im) 1))
1.0ms	(fma x.re y.re (* x.im y.im))
11.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series372.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (* (hypot y.re y.im) 1))
36.0ms	(fma x.re y.re (* x.im y.im))
173.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
110.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify46.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (33.0ms)

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

prune243.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	150	7	157
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	157	10	167

Merged error: 5.2b

Counts

167 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(/ (/ (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))
16.5b	(/ (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)
7.0ms	(/ (/ (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))

series299.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot y.re y.im)
109.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
35.0ms	(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))

simplify76.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (66.0ms)

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

prune259.0ms

Filtered

111 candidates to 89 candidates (80.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	109	12	121

Merged error: 5.1b

Counts

121 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt (hypot y.re y.im)))
0.3b	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))))
7.3b	(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
9.4b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

5792×	`times-frac`
2471×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1329×	`sqrt-prod`
172×	`div-inv`
105×	`associate-/r*`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
31×	`associate-/l*`
25×	`associate-/r/`
20×	`cbrt-undiv`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
1×	`sqrt-pow1` `pow1/2` `associate-/l/` `inv-pow`

Counts

4 → 1883

Calls

4 calls:

4.0ms	(/ 1 (sqrt (hypot y.re y.im)))
50.0ms	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))))
8.0ms	(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

series610.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ 1 (sqrt (hypot y.re y.im)))
175.0ms	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))))
153.0ms	(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
204.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

simplify686.0ms

Algorithm

egg-herbie

Counts

1895 → 1895

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5002	49275

prune5.0s

Filtered

1895 candidates to 1237 candidates (65.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	1892	3	1895
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	1893	14	1907

Merged error: 4.7b

Counts

1907 → 14

regimes234.0ms

Accuracy

29.2% (8.2b remaining)

Error of 13.9b against oracle of 5.7b and baseline of 17.2b

bsearch63.0ms

Steps

Iters	Range		Point
5	1.3815484546578421e+73	3.4258758800285786e+73	3.3703509945803273e+73
7	-5.748822937396627e+92	-3.149463098646164e+91	-4.7598287961022074e+92

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

sample589.0ms

Algorithm

intervals

Results

372.0ms

8488×

body

valid