Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

269×

body

valid

simplify12.0ms

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
done	94	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize13.0ms

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))
25.5b	(/ (- (* 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))
27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series161.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
42.0ms	(- (* x.im y.re) (* x.re y.im))
92.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify37.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	316	555
1	1343	496
2	5001	481
done	5001	481

prune184.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 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))
16.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite85.0ms

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:

54.0ms	(* (/ 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))
19.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series346.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
41.0ms	(- (* x.im y.re) (* x.re y.im))
120.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify56.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (46.0ms)

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

prune262.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize11.0ms

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) 1))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite54.0ms

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:

22.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
8.0ms	(- (* x.im y.re) (* x.re y.im))
19.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series286.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(/ (/ (- (* 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))
122.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify50.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (37.0ms)

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

prune272.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.5b	(- (* x.im y.re) (* x.re y.im))
17.0b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
29×	`add-cbrt-cube`
26×	`prod-exp`
23×	`div-exp`
18×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity` `times-frac`
11×	`add-cube-cbrt`
9×	`cbrt-undiv` `1-exp` `cbrt-unprod`
6×	`associate-/l/`
5×	`pow1` `flip3--` `flip--` `add-log-exp`
4×	`frac-times` `rec-exp` `associate-*l/`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `unswap-sqr`
2×	`associate-*r/` `un-div-inv` `div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

3 → 100

Calls

3 calls:

27.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
8.0ms	(- (* x.im y.re) (* x.re y.im))
33.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
40.0ms	(- (* x.im y.re) (* x.re y.im))
118.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

simplify57.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	515	952
1	2244	748
2	5003	729
done	5003	729

prune218.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 6.1b

regimes241.0ms

Accuracy

26.4% (9.0b remaining)

Error of 13.9b against oracle of 4.9b and baseline of 17.2b

bsearch63.0ms

Steps

Iters	Range		Point
10	4.798752560252719e+112	3.8564235113666274e+122	3.2100008695553146e+117
6	-7.922501144416864e+66	-5.906598016548616e+65	-7.723814496095852e+66

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	32	15
2	32	15
done	32	15

end0.0ms

sample566.0ms

Algorithm

intervals

Results

285.0ms

8466×

body

valid