Details

sample1.7s

Algorithm

intervals

Results

115.0ms	193×	body	80	valid
73.0ms	15×	body	5120	valid
46.0ms	18×	body	2560	valid
35.0ms	17×	body	1280	valid
17.0ms	8×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify944.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	15
1	17	15
2	24	15
3	30	15
4	35	15
done	35	15

prune66.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize244.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite1.2s

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

Counts

4 → 54

Calls

4 calls:

119.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
25.0ms	(+ (* re re) (* im im))
587.0ms	(- (sqrt (+ (* re re) (* im im))) re)
324.0ms	(sqrt (+ (* re re) (* im im)))

series1.9s

Counts

4 → 12

Calls

4 calls:

758.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
169.0ms	(+ (* re re) (* im im))
136.0ms	(- (sqrt (+ (* re re) (* im im))) re)
781.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.9s

Counts

66 → 66

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	114	942
1	277	836
2	1270	752
done	5001	729

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.3b

localize49.0ms

Local error

Found 4 expressions with local error:

10.5b	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
29.5b	(sqrt (+ (* re re) (* im im)))
29.5b	(sqrt (+ (* re re) (* im im)))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite661.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

585.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
33.0ms	(sqrt (+ (* re re) (* im im)))
15.0ms	(sqrt (+ (* re re) (* im im)))
25.0ms	(sqrt (+ (* re re) (* im im)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
76.0ms	(sqrt (+ (* re re) (* im im)))
136.0ms	(sqrt (+ (* re re) (* im im)))
270.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.9s

Counts

69 → 69

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	64	1227
1	150	1131
2	398	665
3	1455	626
done	5001	618

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.3b

localize162.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
27.9b	(sqrt (* 2.0 (+ (* im im) 0)))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite497.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv`

Counts

4 → 96

Calls

4 calls:

126.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
317.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
19.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
28.0ms	(sqrt (+ (* re re) (* im im)))

series1.1s

Counts

4 → 12

Calls

4 calls:

800.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
83.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
73.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
67.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.6s

Counts

108 → 108

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	198	2506
1	462	2091
2	2073	1954
done	5002	1936

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.9b

localize369.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite985.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
46×	`times-frac`
39×	`sqrt-prod`
37×	`add-cube-cbrt`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1` `associate-/r*`
6×	`sqrt-div` `associate-l` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 125

Calls

4 calls:

74.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
656.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
61.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
23.0ms	(sqrt (+ (* re re) (* im im)))

series1.8s

Counts

4 → 12

Calls

4 calls:

504.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
977.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
142.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
146.0ms	(sqrt (+ (* re re) (* im im)))

simplify12.6s

Counts

137 → 137

Iterations

Useful iterations: done (12.5s)

Iter	Nodes	Cost
0	248	2920
1	651	2642
2	4131	2474
done	5001	2468

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.6b

regimes1.3s

Accuracy

67.7% (9.6b remaining)

Error of 18.0b against oracle of 8.4b and baseline of 38.1b

bsearch833.0ms

Steps

Iters	Range	Point
8	2.014767095932623e+139	1.7822480901469312e+143	1.0657070915496316e+142
8	-1.2732295527427012e-306	1.2473932975231144e-307	-4.465731634511006e-309
5	-8.063377314207298e+68	-3.963825905852324e+68	-7.993856736562818e+68

Iters

Range

Point

2.014767095932623e+139

1.7822480901469312e+143

1.0657070915496316e+142

-1.2732295527427012e-306

1.2473932975231144e-307

-4.465731634511006e-309

-8.063377314207298e+68

-3.963825905852324e+68

-7.993856736562818e+68

simplify105.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	44	97
1	56	97
done	56	97

end0.0ms

sample17.9s

Algorithm

intervals

Results

5.8s	667×	body	2560	valid
5.2s	6036×	body	80	valid
2.5s	314×	body	5120	valid
1.9s	483×	body	1280	valid
1.8s	275×	body	640	valid
118.0ms	144×	body	320	valid
15.0ms	81×	body	160	valid