Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

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: 24.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
24.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series130.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (* x.im y.re) (* x.re y.im))
91.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify109.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	270	481
1	1012	432
2	3842	422
3	5001	421

prune155.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.7b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite84.0ms

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:

0.0ms	(hypot y.re y.im)
51.0ms	(* (/ 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))
20.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series403.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot y.re y.im)
189.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
39.0ms	(- (* x.im y.re) (* x.re y.im))
124.0ms	(/ (- (* 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

prune333.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize11.0ms

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) 1))
0.7b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

0.0ms	(hypot y.re y.im)
23.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
9.0ms	(- (* x.im y.re) (* x.re y.im))
18.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series337.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot y.re y.im)
130.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
39.0ms	(- (* x.im y.re) (* x.re y.im))
121.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	432	989
1	1706	876
2	5002	875

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
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) 1))
8.9b	(/ (* x.im y.re) (hypot y.re y.im))
10.4b	(/ (* x.re y.im) (hypot y.re y.im))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

57×	`times-frac`
49×	`prod-diff`
46×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
24×	`div-inv`
21×	`add-exp-log`
19×	`add-cbrt-cube`
8×	`associate-/l*`
7×	`fma-neg` `div-exp` `associate-/r*`
6×	`cbrt-undiv` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `prod-exp` `log1p-expm1-u` `associate-/l/`
3×	`distribute-rgt-out--` `frac-2neg` `clear-num` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `1-exp` `div-sub`

Counts

4 → 156

Calls

4 calls:

22.0ms	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
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) 1))
12.0ms	(/ (* x.im y.re) (hypot y.re y.im))
9.0ms	(/ (* x.re y.im) (hypot y.re y.im))

series606.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
255.0ms	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))) (* (hypot y.re y.im) 1))
72.0ms	(/ (* x.im y.re) (hypot y.re y.im))
76.0ms	(/ (* x.re y.im) (hypot y.re y.im))

simplify84.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	622	2347
1	2999	1732
2	5002	1678

prune358.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes146.0ms

Accuracy

0% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	31
1	38	31
2	38	31

end0.0ms

sample605.0ms

Algorithm

intervals

Results

298.0ms

8478×

body

valid