Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

263×

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: 24.3b

localize13.0ms

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))
23.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite44.0ms

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))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
43.0ms	(- (* x.im y.re) (* x.re y.im))
89.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify41.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (34.0ms)

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

prune184.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.8b

localize13.0ms

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))
15.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite83.0ms

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)
52.0ms	(* (/ 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))

series387.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot y.re y.im)
182.0ms	(* (/ 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))
118.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify60.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (50.0ms)

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

prune310.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

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))
15.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite54.0ms

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)
21.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
9.0ms	(- (* x.im y.re) (* x.re y.im))
19.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series330.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot y.re y.im)
125.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
38.0ms	(- (* x.im y.re) (* x.re y.im))
120.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify51.0ms

Counts

143 → 143

Iterations

Useful iterations: 2 (38.0ms)

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

prune368.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
0.7b	(- (* x.im y.re) (* x.re y.im))
15.8b	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

249×	`add-exp-log`
171×	`times-frac`
120×	`div-exp`
112×	`prod-exp`
109×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
95×	`add-cube-cbrt`
64×	`1-exp`
50×	`associate-r`
47×	`add-cbrt-cube`
43×	`rec-exp`
19×	`cbrt-undiv`
18×	`associate-/r*` `associate-/r/`
12×	`pow1` `cbrt-unprod`
11×	`div-inv`
9×	`flip3--` `flip--`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
5×	`pow-flip` `pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`inv-pow`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-r/` `prod-diff` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 292

Calls

4 calls:

20.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
81.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
10.0ms	(- (* x.im y.re) (* x.re y.im))
12.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
182.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
41.0ms	(- (* x.im y.re) (* x.re y.im))
94.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify100.0ms

Counts

304 → 304

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	1165	3311
1	4700	2898
2	5002	2690
done	5002	2690

prune531.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.6b

regimes215.0ms

Accuracy

33.6% (8.2b remaining)

Error of 12.8b against oracle of 4.6b and baseline of 17.0b

bsearch148.0ms

Steps

Iters	Range		Point
10	4.541079568123855e+144	5.674313332642103e+157	1.0416619596575744e+152
6	3.3667777604995706e+128	2.1415160322372948e+129	2.1133355762605848e+129
10	2.7964112558181106e-143	1.9991076826110307e-133	3.688197923953055e-142
9	-1.8943269263904516e+161	-1.2073983107934418e+155	-8.245974705788371e+157

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	32
1	53	32
2	56	32
3	56	32
done	56	32

end0.0ms

sample593.0ms

Algorithm

intervals

Results

298.0ms

8471×

body

valid