Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

268×

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: 28.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
27.9b	(/ (- (* 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:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* y.re y.re) (* y.im y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
85.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (33.0ms)

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

prune197.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.0b

localize12.0ms

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)))
0.3b	(- (* x.im y.re) (* x.re y.im))
18.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite29.0ms

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:

1.0ms	(hypot y.re y.im)
15.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
4.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series392.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot y.re y.im)
191.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
37.0ms	(- (* x.im y.re) (* x.re y.im))
118.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify60.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (49.0ms)

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

prune329.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
18.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `hypot-udef` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 131

Calls

4 calls:

1.0ms	(hypot y.re y.im)
7.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
5.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series313.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
112.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
35.0ms	(- (* x.im y.re) (* x.re y.im))
117.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify49.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	460	1435
1	1669	1331
2	5001	1322

prune369.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
0.4b	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
18.2b	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

528×	`times-frac`
255×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
56×	`associate-/l*`
39×	`associate-/r/`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
21×	`associate-/r*`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `associate-/l/` `inv-pow`

Counts

4 → 359

Calls

4 calls:

15.0ms	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
5.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
116.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
90.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1296	5404
1	5002	4894

prune798.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

regimes221.0ms

Accuracy

22.7% (9.2b remaining)

Error of 14.0b against oracle of 4.7b and baseline of 16.7b

bsearch139.0ms

Steps

Iters	Range	Point
8	6.736236834044166e+174	2.543242481922855e+177	6.8023434970335964e+174
9	-5.99961992380576e-270	-2.2239357130567353e-275	-1.0119004740350262e-272
8	-4.617021828322126e+139	-2.519325379392933e+135	-4.286619182115773e+139

Iters

Range

Point

6.736236834044166e+174

2.543242481922855e+177

6.8023434970335964e+174

-5.99961992380576e-270

-2.2239357130567353e-275

-1.0119004740350262e-272

-4.617021828322126e+139

-2.519325379392933e+135

-4.286619182115773e+139

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	22
1	39	22
2	39	22

end0.0ms

sample527.0ms

Algorithm

intervals

Results

310.0ms

8469×

body

valid