Details

sample191.0ms

Algorithm

intervals

Results

50.0ms	20×	body	1280	valid
24.0ms	176×	body	80	valid
24.0ms	29×	body	2560	valid
10.0ms	11×	body	5120	valid
6.0ms	11×	body	640	valid
2.0ms	7×	body	160	valid
1.0ms	2×	body	320	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	35
4	35
3	30
2	24
1	17
0	12

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.5b	(- (sqrt (+ (* re re) (* im im))) re)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`sqrt-pow1`
2×	`flip3-+` `flip3--` `pow1/2` `associate-*r/` `flip-+` `flip--` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `diff-log` `pow-prod-down` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

15.0ms	(+ (* re re) (* im im))
36.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (+ (* re re) (* im im)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* re re) (* im im))
269.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
97.0ms	(- (sqrt (+ (* re re) (* im im))) re)
78.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
3	3038
2	811
1	260
0	114

prune658.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
0.3b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
27.2b	(sqrt (* 2.0 (+ (* im im) 0)))
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
32×	`sqrt-prod`
28×	`times-frac`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
8×	`pow1` `sqrt-div`
7×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-r/` `associate-/l`
3×	`sqrt-pow1`
2×	`pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sum-log` `frac-2neg` `div-exp` `pow-prod-down` `div-inv`

Counts

4 → 96

Calls

4 calls:

29.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
43.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
275.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
57.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
3	3120
2	1090
1	441
0	197

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
0.5b	(/ (sqrt 2.0) (/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im)))
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

318×	`times-frac`
223×	`*-un-lft-identity`
181×	`sqrt-prod`
172×	`add-sqr-sqrt`
171×	`add-cube-cbrt`
28×	`associate-/r*`
26×	`distribute-lft-out`
13×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `sqrt-div` `div-exp`
3×	`flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/r/`

Counts

4 → 268

Calls

4 calls:

48.0ms	(/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im))
24.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(/ (sqrt 2.0) (/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series574.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im))
80.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
260.0ms	(/ (sqrt 2.0) (/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im)))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

280 → 280

Iterations

Iter	Nodes
2	2537
1	949
0	374

prune3.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (* (cbrt (sqrt 2.0)) (fabs im)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
21×	`add-cbrt-cube`
20×	`*-un-lft-identity`
15×	`sqrt-prod`
14×	`times-frac`
13×	`add-sqr-sqrt` `associate-l`
12×	`prod-exp` `add-cube-cbrt` `cbrt-unprod`
10×	`pow1`
7×	`associate-/r*`
6×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+` `distribute-lft-out`
3×	`pow-prod-down`
2×	`div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l/` `-commutative` `associate-/l*`

Counts

4 → 95

Calls

4 calls:

31.0ms	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
122.0ms	(* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (* (cbrt (sqrt 2.0)) (fabs im)))
18.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
243.0ms	(* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (* (cbrt (sqrt 2.0)) (fabs im)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify629.0ms

Counts

107 → 107

Iterations

Iter	Nodes
2	2256
1	614
0	219

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

regimes673.0ms

Accuracy

68.3% (9.4b remaining)

Error of 17.6b against oracle of 8.2b and baseline of 37.8b

bsearch353.0ms

Steps

Iters	Range		Point
10	1.5347927881719531e+137	1.0303134579162717e+148	7.387383225171874e+137
9	8.078157939339514e-228	5.9061123396576155e-223	8.828385981385365e-228
10	-7.074938547279042e-300	4.152164446645693e-307	-1.2465139226076545e-304
6	-5.294928744263152e+64	-1.2512193358901006e+64	-4.544356418821128e+64

simplify29.0ms

Iterations

Iter	Nodes
2	63
1	63
0	50

end0.0ms

sample3.0s

Algorithm

intervals

Results

915.0ms	6054×	body	80	valid
724.0ms	271×	body	5120	valid
602.0ms	673×	body	2560	valid
310.0ms	510×	body	1280	valid
192.0ms	283×	body	640	valid
45.0ms	132×	body	320	valid
21.0ms	77×	body	160	valid