Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

277×

body

valid

simplify12.0ms

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: 27.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.8b	(- (* x.im y.re) (* x.re y.im))
26.6b	(/ (- (* x.im y.re) (* x.re 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`
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:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
34.0ms	(- (* x.im y.re) (* x.re y.im))
82.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (32.0ms)

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

prune197.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.8b	(- (* x.im y.re) (* x.re y.im))
15.5b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log`
38×	`prod-exp`
32×	`add-cbrt-cube`
29×	`div-exp`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`1-exp`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`pow1` `rec-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`flip3--` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

5.0ms	(/ 1 (* (hypot y.re y.im) 1))
27.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series376.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1 (* (hypot y.re y.im) 1))
175.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
38.0ms	(- (* x.im y.re) (* x.re y.im))
113.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify59.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	555	1207
1	2306	1003
2	5003	995

prune353.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.8b	(- (* x.im y.re) (* x.re y.im))
15.5b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite22.0ms

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

Counts

3 → 99

Calls

3 calls:

10.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series266.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
40.0ms	(- (* x.im y.re) (* x.re y.im))
111.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify48.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	423	962
1	1691	852
2	5001	851

prune281.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.2b	(* (* 1 (/ 1 (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.8b	(- (* x.im y.re) (* x.re y.im))
15.5b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
34×	`prod-exp`
29×	`add-cbrt-cube`
27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
20×	`div-exp`
13×	`1-exp` `associate-r`
10×	`pow1` `cbrt-unprod`
7×	`cbrt-undiv`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`rec-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-*r/` `pow-prod-down` `div-inv`
2×	`frac-times` `flip3--` `frac-2neg` `associate-*l/` `clear-num` `un-div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `*-commutative` `inv-pow`

Counts

4 → 136

Calls

4 calls:

2.0ms	(/ 1 (hypot y.re y.im))
21.0ms	(* (* 1 (/ 1 (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series367.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1 (hypot y.re y.im))
174.0ms	(* (* 1 (/ 1 (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
38.0ms	(- (* x.im y.re) (* x.re y.im))
108.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify57.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	536	1146
1	1969	932
2	5001	909

prune291.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.0b

regimes236.0ms

Accuracy

32.1% (8.4b remaining)

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

bsearch107.0ms

Steps

Iters	Range	Point
8	2.5697366854017785e+130	7.599228493726907e+133	9.805410313753759e+132
7	-1.0127169747952713e-97	-3.5554999740842237e-99	-4.1054268527148993e-98
8	-5.294872751913314e+157	-4.107841816162241e+153	-1.3657760091869803e+154

Iters

Range

Point

2.5697366854017785e+130

7.599228493726907e+133

9.805410313753759e+132

-1.0127169747952713e-97

-3.5554999740842237e-99

-4.1054268527148993e-98

-5.294872751913314e+157

-4.107841816162241e+153

-1.3657760091869803e+154

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

sample501.0ms

Algorithm

intervals

Results

293.0ms

8494×

body

valid