Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

276×

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.9b	(+ (* x.re y.re) (* x.im y.im))
29.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

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:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series131.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* y.re y.re) (* y.im y.im))
32.0ms	(+ (* x.re y.re) (* x.im y.im))
74.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify139.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (32.0ms)

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

prune211.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.8b	(fma x.re y.re (* x.im y.im))
19.1b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite74.0ms

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:

11.0ms	(/ 1 (* (hypot y.re y.im) 1))
49.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.0ms	(fma x.re y.re (* x.im y.im))
8.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series353.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1 (* (hypot y.re y.im) 1))
164.0ms	(* (/ 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))
105.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify47.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (34.0ms)

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

prune274.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.8b	(fma x.re y.re (* x.im y.im))
19.1b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

13.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms	(fma x.re y.re (* x.im y.im))
7.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series247.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
34.0ms	(fma x.re y.re (* x.im y.im))
104.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify72.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670

prune250.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.4b

localize17.0ms

Local error

Found 4 expressions with local error:

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)))
0.8b	(fma x.re y.re (* x.im y.im))
9.5b	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
10.0b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

109.0ms	(* (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)))
0.0ms	(fma x.re y.re (* x.im y.im))
33.0ms	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
34.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (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)))
35.0ms	(fma x.re y.re (* x.im y.im))
248.0ms	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
158.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	404	1276
1	2076	1059
2	5001	1017

prune332.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 8.4b

regimes213.0ms

Accuracy

26.6% (8.3b remaining)

Error of 13.8b against oracle of 5.5b and baseline of 16.8b

bsearch116.0ms

Steps

Iters	Range		Point
5	2.086626702119805e+103	6.10127295373237e+103	5.498440485625483e+103
8	8.316403660619846e-298	4.099118401478167e-294	8.498893419169804e-298
8	-1.108464524242474e-248	-8.801717042137143e-253	-8.946923930155794e-253
6	-5.504824555336891e+149	-5.650723842587128e+148	-8.628922924620212e+148

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	24
1	37	24
2	37	24

end0.0ms

sample556.0ms

Algorithm

intervals

Results

273.0ms

8493×

body

valid