Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

276×

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: 28.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
27.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite45.0ms

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))
28.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series138.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
33.0ms	(- (* x.im y.re) (* x.re y.im))
79.0ms	(/ (- (* 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

prune177.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.3b

localize11.0ms

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)))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite97.0ms

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:

11.0ms	(/ 1 (* (hypot y.re y.im) 1))
52.0ms	(* (/ 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))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series353.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1 (* (hypot y.re y.im) 1))
165.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
32.0ms	(- (* x.im y.re) (* x.re y.im))
106.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify61.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (49.0ms)

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

prune307.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize9.0ms

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))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite51.0ms

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:

21.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
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))

series245.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
33.0ms	(- (* x.im y.re) (* x.re y.im))
105.0ms	(/ (- (* 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 (37.0ms)

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

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))) (hypot y.re y.im))
9.1b	(/ (* x.im y.re) (hypot y.re y.im))
14.1b	(/ (* x.re y.im) (hypot y.re y.im))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`times-frac`
18×	`add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube`
11×	`div-inv`
9×	`associate-/r*`
8×	`associate-/l*`
5×	`cbrt-undiv` `div-exp`
4×	`distribute-rgt-out--` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`
1×	`flip3--` `div-sub` `frac-sub` `flip--` `sub-div`

Counts

3 → 92

Calls

3 calls:

57.0ms	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))) (hypot y.re y.im))
9.0ms	(/ (* x.im y.re) (hypot y.re y.im))
9.0ms	(/ (* x.re y.im) (hypot y.re y.im))

series344.0ms

Counts

3 → 9

Calls

3 calls:

218.0ms	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))) (hypot y.re y.im))
61.0ms	(/ (* x.im y.re) (hypot y.re y.im))
65.0ms	(/ (* x.re y.im) (hypot y.re y.im))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	378	858
1	1628	771
2	5001	769

prune231.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.7b

regimes167.0ms

Accuracy

55.9% (3.9b remaining)

Error of 4.5b against oracle of 0.6b and baseline of 9.5b

bsearch68.0ms

Steps

Iters	Range		Point
9	4.90289116134144e+65	1.2323468673482036e+72	5.303929542037185e+69
7	-3.6597854604479168e+53	-9.307728119781708e+51	-2.2571318052192643e+53

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample548.0ms

Algorithm

intervals

Results

277.0ms

8493×

body

valid