Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

276×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
27.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

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`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

3 → 64

Calls

3 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series147.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* y.re y.re) (* y.im y.im))
38.0ms	(- (* x.im y.re) (* x.re y.im))
84.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	316	555
1	1343	496
2	5001	481

prune198.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.4b

localize218.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.7b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
32×	`prod-exp`
27×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `rec-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `hypot-udef` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 120

Calls

4 calls:

0.0ms	(hypot y.re y.im)
53.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
8.0ms	(- (* x.im y.re) (* x.re y.im))
19.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series362.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot y.re y.im)
172.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
34.0ms	(- (* x.im y.re) (* x.re y.im))
107.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify61.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	546	1122
1	2249	931
2	5002	929

prune318.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.7b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite53.0ms

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`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `hypot-udef` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 109

Calls

4 calls:

0.0ms	(hypot y.re y.im)
24.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
8.0ms	(- (* x.im y.re) (* x.re y.im))
18.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series307.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot y.re y.im)
113.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
35.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	432	989
1	1705	876
2	5001	875

prune322.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (sqrt (hypot y.re y.im)) (hypot y.re y.im)))
0.7b	(- (* x.im y.re) (* x.re y.im))
8.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
17.6b	(* (/ 1 (* (sqrt (hypot y.re y.im)) (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
45×	`add-sqr-sqrt`
44×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-cbrt-cube`
23×	`prod-exp`
22×	`associate-r` `sqrt-prod`
20×	`div-exp`
13×	`pow1`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
7×	`pow-flip` `associate-l` `associate-/r*`
6×	`rec-exp` `1-exp` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`unswap-sqr`
2×	`flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `clear-num` `pow-prod-up` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `cube-unmult` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 161

Calls

4 calls:

16.0ms	(/ 1 (* (sqrt (hypot y.re y.im)) (hypot y.re y.im)))
8.0ms	(- (* x.im y.re) (* x.re y.im))
19.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
70.0ms	(* (/ 1 (* (sqrt (hypot y.re y.im)) (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ 1 (* (sqrt (hypot y.re y.im)) (hypot y.re y.im)))
33.0ms	(- (* x.im y.re) (* x.re y.im))
190.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
175.0ms	(* (/ 1 (* (sqrt (hypot y.re y.im)) (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))

simplify83.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	649	1820
1	3069	1536
2	5001	1430

prune406.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

regimes187.0ms

Accuracy

32.2% (8.4b remaining)

Error of 13.2b against oracle of 4.8b and baseline of 17.2b

bsearch117.0ms

Steps

Iters	Range	Point
9	1.0826531041751224e+149	1.7435338617608826e+156	1.368280955057291e+154
7	1.1952581674532207e-17	4.3612806898142137e-16	1.0980505939332989e-16
11	-3.555858957855583e+230	-3.907040633350073e+205	-5.457377104622506e+208

Iters

Range

Point

1.0826531041751224e+149

1.7435338617608826e+156

1.368280955057291e+154

1.1952581674532207e-17

4.3612806898142137e-16

1.0980505939332989e-16

-3.555858957855583e+230

-3.907040633350073e+205

-5.457377104622506e+208

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	42	24
2	42	24

end0.0ms

sample582.0ms

Algorithm

intervals

Results

301.0ms

8506×

body

valid