Details

sample40.0ms

Algorithm

intervals

Results

29.0ms

269×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 22.4b

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))
21.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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))
11.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
86.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (32.0ms)

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

prune204.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize12.0ms

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)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.3b	(- (* x.im y.re) (* x.re y.im))
14.1b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite43.0ms

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:

4.0ms	(/ 1 (* (hypot y.re y.im) 1))
24.0ms	(* (/ 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))

series390.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (* (hypot y.re y.im) 1))
182.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
36.0ms	(- (* x.im y.re) (* x.re y.im))
117.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify64.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (52.0ms)

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

prune327.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

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))
0.3b	(- (* x.im y.re) (* x.re y.im))
14.1b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 121

Calls

3 calls:

9.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.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))

series268.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
115.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	451	1408
1	1659	1307
2	5001	1298

prune373.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
0.3b	(- (* x.im y.re) (* x.re y.im))
14.2b	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

249×	`add-exp-log`
171×	`times-frac`
120×	`div-exp`
112×	`prod-exp`
109×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
95×	`add-cube-cbrt`
64×	`1-exp`
50×	`associate-r`
47×	`add-cbrt-cube`
43×	`rec-exp`
19×	`cbrt-undiv`
18×	`associate-/r*` `associate-/r/`
12×	`pow1` `cbrt-unprod`
11×	`div-inv`
9×	`flip3--` `flip--`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
5×	`pow-flip` `pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`inv-pow`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-r/` `prod-diff` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 292

Calls

4 calls:

9.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
44.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
3.0ms	(- (* x.im y.re) (* x.re y.im))
5.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
180.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
38.0ms	(- (* x.im y.re) (* x.re y.im))
89.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	1166	3296
1	4671	2898
2	5003	2690

prune536.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

regimes191.0ms

Accuracy

14.4% (10.0b remaining)

Error of 14.5b against oracle of 4.6b and baseline of 16.2b

bsearch61.0ms

Steps

Iters	Range		Point
10	1.6744273082514658e+93	2.0995339615643966e+103	1.5173701027657723e+98

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	33	14
2	34	14
3	34	14

end0.0ms

sample1.1s

Algorithm

intervals

Results

832.0ms

8472×

body

valid