Details

sample38.0ms

Algorithm

intervals

Results

26.0ms

271×

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: 28.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
28.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

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:

3.0ms	(- (* x.im y.re) (* x.re y.im))
11.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- (* 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)))

simplify106.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (100.0ms)

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

prune155.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x.im y.re) (* x.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)))
15.2b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`prod-exp`
26×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`rec-exp`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 110

Calls

3 calls:

3.0ms	(- (* x.im y.re) (* x.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)))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series339.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(- (* x.im y.re) (* x.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)))
119.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify66.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	537	1095
1	2236	907
2	5002	905

prune292.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
15.2b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 99

Calls

3 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series274.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(- (* x.im y.re) (* x.re y.im))
117.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
115.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify48.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	423	962
1	1691	852
2	5001	851

prune299.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt (hypot y.re y.im)))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
7.5b	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
7.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

406×	`add-exp-log`
232×	`prod-exp`
145×	`div-exp`
108×	`add-sqr-sqrt`
97×	`times-frac`
89×	`add-cbrt-cube`
77×	`1-exp`
68×	`*-un-lft-identity`
62×	`add-cube-cbrt`
53×	`sqrt-prod`
50×	`rec-exp`
36×	`cbrt-unprod`
29×	`associate-l`
28×	`cbrt-undiv`
23×	`associate-r`
15×	`unswap-sqr`
13×	`pow1`
12×	`associate-/r*`
6×	`frac-times` `associate-r/` `associate-/l`
5×	`div-inv`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/`
1×	`flip3--` `sqrt-pow1` `pow1/2` `div-sub` `flip--` `inv-pow`

Counts

4 → 308

Calls

4 calls:

3.0ms	(/ 1 (sqrt (hypot y.re y.im)))
47.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
30.0ms	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 1 (sqrt (hypot y.re y.im)))
195.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
119.0ms	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
201.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1253	4287
1	5001	3428

prune541.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.9b

regimes229.0ms

Accuracy

17% (10.5b remaining)

Error of 14.9b against oracle of 4.4b and baseline of 17.1b

bsearch39.0ms

Steps

Iters	Range		Point
6	1.7888846860341737e+184	2.0183165039998653e+185	4.644327594217982e+184

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	12
1	29	12
2	29	12

end0.0ms

sample1.1s

Algorithm

intervals

Results

832.0ms

8517×

body

valid