Details

sample82.0ms

Algorithm

intervals

Results

22.0ms	190×	body	80	valid
16.0ms	15×	body	1280	valid
16.0ms	25×	body	2560	valid
10.0ms	12×	body	5120	valid
3.0ms	8×	body	640	valid
2.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	24
2	24
1	22
0	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`sqrt-div` `add-cube-cbrt` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow-prod-down` `distribute-lft-out`

Counts

3 → 43

Calls

3 calls:

34.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
60.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
13.0ms	(sqrt (+ (* re re) (* im im)))

series412.0ms

Counts

3 → 9

Calls

3 calls:

262.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
83.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
67.0ms	(sqrt (+ (* re re) (* im im)))

simplify668.0ms

Counts

52 → 52

Iterations

Iter	Nodes
3	2046
2	680
1	245
0	102

prune276.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
27.3b	(sqrt (* 2.0 (+ (* im im) 0)))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`times-frac`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-/r*`
8×	`pow1` `sqrt-div`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`associate-r/` `insert-posit16` `associate-/l`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `div-inv`

Counts

4 → 113

Calls

4 calls:

75.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
10.0ms	(sqrt (+ (* re re) (* im im)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
77.0ms	(- (sqrt (+ (* re re) (* im im))) re)
51.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

125 → 125

Iterations

Iter	Nodes
3	3360
2	1095
1	450
0	216

prune703.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (fabs im))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `times-frac`
7×	`pow1`
6×	`associate-l` `add-log-exp` `difference-of-squares`
4×	`sqrt-div` `insert-posit16`
3×	`associate-r` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 91

Calls

4 calls:

55.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(* (sqrt 2.0) (fabs im))
43.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (+ (* re re) (* im im)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(* (sqrt 2.0) (fabs im))
55.0ms	(- (sqrt (+ (* re re) (* im im))) re)
62.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts

103 → 103

Iterations

Iter	Nodes
3	7092
2	1555
1	459
0	194

prune592.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im)))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

27×	`sqrt-prod`
25×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
12×	`add-cube-cbrt`
10×	`pow1`
9×	`associate-/r` `times-frac` `associate-l*`
6×	`prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares`
4×	`sqrt-div` `insert-posit16`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `distribute-lft-out--`
2×	`flip3--` `associate-/r/` `flip--`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 95

Calls

4 calls:

75.0ms	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
24.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im)))
35.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im)))
68.0ms	(- (sqrt (+ (* re re) (* im im))) re)
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.0s

Counts

107 → 107

Iterations

Iter	Nodes
3	8376
2	1820
1	520
0	203

prune577.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.3b

regimes650.0ms

Accuracy

69.1% (9.0b remaining)

Error of 16.5b against oracle of 7.4b and baseline of 36.6b

bsearch788.0ms

Steps

Iters	Range	Point
9	4.7599761429228367e+98	9.416899659600005e+104	9.299865300702547e+104
9	-2.3066181393648038e-248	-3.0719470799760817e-257	-3.1198242249434154e-257
10	-5.119440634421198e+122	-1.7867168956050676e+111	-3.2601941440528353e+122

Iters

Range

Point

4.7599761429228367e+98

9.416899659600005e+104

9.299865300702547e+104

-2.3066181393648038e-248

-3.0719470799760817e-257

-3.1198242249434154e-257

-5.119440634421198e+122

-1.7867168956050676e+111

-3.2601941440528353e+122

simplify15.0ms

Iterations

Iter	Nodes
2	55
1	55
0	42

end0.0ms

sample2.5s

Algorithm

intervals

Results

749.0ms	5970×	body	80	valid
678.0ms	703×	body	2560	valid
328.0ms	307×	body	5120	valid
268.0ms	481×	body	1280	valid
125.0ms	289×	body	640	valid
124.0ms	167×	body	320	valid
17.0ms	83×	body	160	valid