Details

sample29.0ms

Algorithm

intervals

Results

16.0ms

269×

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
25.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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))
5.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series49.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
12.0ms	(- (* x.im y.re) (* x.re y.im))
32.0ms	(/ (- (* 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

prune553.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.0b

localize11.0ms

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)))
0.7b	(- (* x.im y.re) (* x.re y.im))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite38.0ms

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)
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))

series104.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(hypot y.re y.im)
42.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
11.0ms	(- (* x.im y.re) (* x.re y.im))
44.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify59.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (48.0ms)

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

prune907.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.3b

localize10.0ms

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))
0.7b	(- (* x.im y.re) (* x.re y.im))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite24.0ms

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:

0.0ms	(hypot y.re y.im)
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))

series108.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(hypot y.re y.im)
45.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
11.0ms	(- (* x.im y.re) (* x.re y.im))
44.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify51.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (37.0ms)

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

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.3b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (* (sqrt (/ 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))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `associate-l` `add-cbrt-cube`
16×	`sqrt-prod`
14×	`associate-r`
11×	`pow1`
10×	`sqrt-div`
7×	`prod-exp` `cbrt-unprod`
6×	`frac-times` `associate-*r/` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
2×	`flip3--` `*-commutative` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num`

Counts

4 → 129

Calls

4 calls:

26.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
61.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (* (sqrt (/ 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))

series163.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
42.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))))
11.0ms	(- (* x.im y.re) (* x.re y.im))
44.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify78.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	527	1554
1	2666	1314
2	5001	1267

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.3b

regimes675.0ms

Accuracy

31.6% (8.7b remaining)

Error of 13.6b against oracle of 4.9b and baseline of 17.7b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	42
1	52	42
2	57	42
3	68	42
4	70	42
5	70	42

end0.0ms

sample741.0ms

Algorithm

intervals

Results

525.0ms

8464×

body

valid