Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

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

prune2.0ms

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)))

rewrite17.0ms

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

series155.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
40.0ms	(- (* x.im y.re) (* x.re y.im))
87.0ms	(/ (- (* 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

prune203.0ms

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))

rewrite39.0ms

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))

series387.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
184.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
35.0ms	(- (* x.im y.re) (* x.re y.im))
120.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify57.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	546	1126
1	2250	931
2	5003	929

prune510.0ms

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) 1))
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))

rewrite23.0ms

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)
10.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
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))

series318.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot y.re y.im)
116.0ms	(/ (/ (- (* 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))
113.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify47.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	432	989
1	1705	876
2	5001	875

prune326.0ms

Pruning

11 alts after pruning (9 fresh and 2 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))

rewrite103.0ms

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:

27.0ms	(* (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))

series608.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
186.0ms	(* (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))))
40.0ms	(- (* x.im y.re) (* x.re y.im))
114.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify79.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (65.0ms)

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

prune403.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.3b

regimes248.0ms

Accuracy

31.8% (8.5b remaining)

Error of 13.4b against oracle of 4.9b and baseline of 17.4b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	35
1	43	35
2	43	35

end0.0ms

sample509.0ms

Algorithm

intervals

Results

292.0ms

8464×

body

valid