Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

274×

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: 26.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
26.0b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite28.0ms

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:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(- (* x.im y.re) (* x.re y.im))
14.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
37.0ms	(- (* x.im y.re) (* x.re y.im))
89.0ms	(/ (- (* 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

prune262.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(- (* x.im y.re) (* x.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)))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite32.0ms

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))
4.0ms	(- (* x.im y.re) (* x.re y.im))
13.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series386.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (* (hypot y.re y.im) 1))
38.0ms	(- (* x.im y.re) (* x.re y.im))
182.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
111.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify63.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (51.0ms)

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

prune340.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize19.0ms

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))
0.2b	(- (* x.im y.re) (* x.re y.im))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite37.0ms

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:

13.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
6.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series265.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
37.0ms	(- (* x.im y.re) (* x.re y.im))
116.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify52.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (38.0ms)

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

prune375.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (* x.im y.re) (hypot y.re y.im)) (hypot y.re y.im))
1.0b	(/ (/ (* x.re y.im) (hypot y.re y.im)) (hypot y.re y.im))
9.1b	(/ (* x.re y.im) (hypot y.re y.im))
12.6b	(/ (* x.im y.re) (hypot y.re y.im))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
14×	`cbrt-undiv` `div-exp`
12×	`associate-/r*` `div-inv`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 146

Calls

4 calls:

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

series283.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (/ (* x.im y.re) (hypot y.re y.im)) (hypot y.re y.im))
69.0ms	(/ (/ (* x.re y.im) (hypot y.re y.im)) (hypot y.re y.im))
70.0ms	(/ (* x.re y.im) (hypot y.re y.im))
71.0ms	(/ (* x.im y.re) (hypot y.re y.im))

simplify57.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	495	1158
1	2166	1010
2	5001	996

prune430.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

regimes194.0ms

Accuracy

52.8% (4.0b remaining)

Error of 4.8b against oracle of 0.8b and baseline of 9.3b

bsearch83.0ms

Steps

Iters	Range		Point
8	4.474924955551132e-38	1.5214700919419666e-35	1.0382708421545201e-35
7	-1.1049075135714818e+81	-5.355145492118649e+78	-2.2616143508082277e+79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	25
1	38	25
2	38	25

end0.0ms

sample522.0ms

Algorithm

intervals

Results

303.0ms

8457×

body

valid