Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

265×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.0b	(+ (* x.re y.re) (* x.im y.im))
24.2b	(/ (+ (* 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:

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)))

series133.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* y.re y.re) (* y.im y.im))
31.0ms	(+ (* x.re y.re) (* x.im y.im))
76.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify131.0ms

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

prune223.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize11.0ms

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)))
0.5b	(fma x.re y.re (* x.im y.im))
13.4b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite39.0ms

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))
22.0ms	(* (/ 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))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series385.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (* (hypot y.re y.im) 1))
179.0ms	(* (/ 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))
113.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify49.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (36.0ms)

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

prune311.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

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))
0.5b	(fma x.re y.re (* x.im y.im))
13.4b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite15.0ms

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:

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

series314.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot y.re y.im)
119.0ms	(/ (/ (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))
110.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify79.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (69.0ms)

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

prune318.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize14.0ms

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) 1)))
0.5b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (sqrt (/ 1 (* (hypot y.re y.im) 1))))
0.5b	(fma x.re y.re (* x.im y.im))
13.4b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

66×	`pow1`
46×	`sqrt-pow1`
41×	`add-exp-log`
38×	`sqrt-prod`
33×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
28×	`pow-flip`
25×	`pow-prod-down`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-exp`
18×	`times-frac`
17×	`associate-r`
14×	`swap-sqr` `pow-prod-up`
13×	`cbrt-unprod`
12×	`sqrt-div`
11×	`associate-l`
10×	`inv-pow`
9×	`div-exp`
8×	`pow1/2` `pow-sqr` `div-inv`
6×	`cbrt-undiv` `frac-times` `associate-*l/`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`1-exp` `associate-/l*`
2×	`*-commutative`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r*` `rem-square-sqrt` `fma-udef`

Counts

4 → 163

Calls

4 calls:

101.0ms	(* (* (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) 1)))
29.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (sqrt (/ 1 (* (hypot y.re y.im) 1))))
0.0ms	(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) 1))

series387.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (* (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) 1)))
57.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (sqrt (/ 1 (* (hypot y.re y.im) 1))))
37.0ms	(fma x.re y.re (* x.im y.im))
113.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify84.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	426	1301
1	2304	915
2	5001	852

prune352.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.2b

regimes229.0ms

Accuracy

35.7% (6.9b remaining)

Error of 12.6b against oracle of 5.7b and baseline of 16.4b

bsearch63.0ms

Steps

Iters	Range		Point
5	2.6545994669624432e+182	1.0129075260036237e+183	5.2660357604755783e+182
9	-2.963931757502914e+119	-3.0087443311191178e+113	-1.0970461090118266e+117

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

sample487.0ms

Algorithm

intervals

Results

276.0ms

8481×

body

valid