Details

sample29.0ms

Algorithm

intervals

Results

16.0ms

267×

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(+ (* x.re y.re) (* x.im y.im))
27.2b	(/ (+ (* 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:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
2.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series49.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
11.0ms	(+ (* x.re y.re) (* x.im y.im))
33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify133.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

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

prune555.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(hypot y.re 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)))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-exp-log`
86×	`prod-exp`
57×	`div-exp`
45×	`add-cbrt-cube`
35×	`1-exp`
16×	`cbrt-unprod`
14×	`cbrt-undiv`
12×	`add-sqr-sqrt` `rec-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`associate-r` `associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`hypot-udef`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
21.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series98.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(hypot y.re y.im)
7.0ms	(hypot y.re y.im)
41.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
43.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify44.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	479	1092
1	1588	808
2	5001	806

prune747.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
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))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite12.0ms

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×	`hypot-udef` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 99

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
6.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
2.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series100.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(hypot y.re y.im)
7.0ms	(hypot y.re y.im)
44.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
42.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify75.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	301	780
1	1076	689
2	3153	689
3	5001	681

prune854.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (* (hypot y.re y.im) 1)))
0.3b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
8.6b	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
9.3b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`add-exp-log` `associate-l` `add-cbrt-cube`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
12×	`pow1`
10×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
5×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-pow1` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-l/` `associate-/r`
2×	`pow-flip` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `frac-times` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-r/` `clear-num` `associate-/l/` `associate-/l` `inv-pow`

Counts

4 → 117

Calls

4 calls:

4.0ms	(sqrt (/ 1 (* (hypot y.re y.im) 1)))
52.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
14.0ms	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
18.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (/ 1 (* (hypot y.re y.im) 1)))
41.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
64.0ms	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
46.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	470	1373
1	2227	1115
2	5001	1054

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.5b

regimes474.0ms

Accuracy

40.1% (6.6b remaining)

Error of 12.7b against oracle of 6.1b and baseline of 17.1b

bsearch40.0ms

Steps

Iters	Range		Point
8	1.2064922412751594e+141	5.462432632406119e+143	8.609811038902364e+142
7	-4.759549154242407e+125	-1.6091628437142707e+124	-3.264789729519792e+125

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

sample741.0ms

Algorithm

intervals

Results

519.0ms

8442×

body

valid