Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	183×	body	80	valid
6.0ms	25×	body	2560	valid
5.0ms	15×	body	5120	valid
4.0ms	20×	body	1280	valid
1.0ms	7×	body	320	valid
1.0ms	4×	body	640	valid
0.0ms	2×	body	160	valid

simplify22.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(- (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

31.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
53.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (+ (* re re) (* im im)))

series293.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify83.0ms

Counts: 52 → 52

prune168.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (sqrt (+ (* re re) (* im im))) re)
5.8b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.4b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

38.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
30.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
55.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
9.0ms	(sqrt (+ (* re re) (* im im)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
211.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
74.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Counts: 111 → 111

prune313.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (sqrt (+ (* re re) (* im im))) re)
5.8b	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
8×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`sqrt-div` `sqrt-prod`
6×	`add-cube-cbrt` `add-log-exp`
5×	`sqrt-pow1`
4×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
3×	`flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`rem-sqrt-square`
1×	`+-commutative` `frac-times` `associate-*l/` `sum-log` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

36.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
182.0ms	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
10.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(sqrt (+ (* re re) (* im im)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
171.0ms	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
38.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify142.0ms

Counts: 69 → 69

prune289.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize19.0ms

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 (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
1.3b	(+ (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

48.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
11.0ms	(* (sqrt 2.0) (fabs (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
42.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
41.0ms	(* (sqrt 2.0) (fabs (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
55.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Counts: 106 → 106

prune353.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

regimes272.0ms

Accuracy

52.3% (17.8b remaining)

Error of 18.2b against oracle of 0.4b and baseline of 37.7b

bsearch331.0ms

Steps

Iters	Range		Point
9	1.5352083456254553e+134	4.290019945054976e+140	2.272841479640385e+138
7	5.607623183418407e-234	1.6557877642610858e-232	7.636046895074116e-234
7	2.52341796223474e-250	5.582398268623716e-249	2.350192530671022e-249
4	1.9447514843596075e-296	3.5660361064754014e-296	2.1106130248162686e-296
6	-1.2013088131739501e-300	-1.0819843522862608e-301	-1.8113892981537156e-301
6	-7.218837226317286e-263	-1.3951434382281519e-263	-2.648694287528554e-263
7	-1.4840491665705872e-183	-1.9343760202872156e-185	-5.89967699622497e-185
10	-7.876869382815934e+47	-1.2380517177182275e+38	-7.760468085811197e+47

simplify2.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

465.0ms	295×	body	5120	valid
341.0ms	5993×	body	80	valid
269.0ms	720×	body	2560	valid
127.0ms	462×	body	1280	valid
52.0ms	162×	body	320	valid
47.0ms	285×	body	640	valid
7.0ms	83×	body	160	valid