Details

sample36.0ms

Algorithm

intervals

Results

9.0ms	188×	body	80	valid
8.0ms	26×	body	2560	valid
4.0ms	16×	body	1280	valid
3.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize68.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite79.0ms

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:

25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
42.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (+ (* re re) (* im im)))

series397.0ms

Counts

3 → 9

Calls

3 calls:

269.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
65.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

52 → 52

Iterations

Iter	Nodes
done	5002
3	2104
2	669
1	246
0	102

prune293.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
16.3b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

37.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
16.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
64.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
11.0ms	(sqrt (+ (* re re) (* im im)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
42.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
68.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	2185
2	749
1	297
0	142

prune379.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 18.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (* 2.0 (+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)))
6.0b	(pow (sqrt E) (log (+ (* re re) (* im im))))
16.3b	(+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)
31.8b	(log (+ (* re re) (* im im)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`log-prod` `unpow-prod-down` `add-exp-log` `add-log-exp`
4×	`log-div` `pow-unpow` `flip3-+` `add-cbrt-cube` `sqrt-prod` `flip-+` `insert-posit16`
3×	`unpow-prod-up` `pow-pow` `sqrt-pow1`
2×	`pow1/2` `sqrt-div` `associate-*r/` `log-pow` `pow-sub`
1×	`pow-to-exp` `+-commutative` `sum-log` `rem-log-exp` `pow-prod-down` `pow-exp` `sqrt-pow2` `distribute-lft-out` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

24.0ms	(sqrt (* 2.0 (+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)))
16.0ms	(pow (sqrt E) (log (+ (* re re) (* im im))))
59.0ms	(+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)
11.0ms	(log (+ (* re re) (* im im)))

series1.1s

Counts

4 → 12

Calls

4 calls:

387.0ms	(sqrt (* 2.0 (+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)))
301.0ms	(pow (sqrt E) (log (+ (* re re) (* im im))))
326.0ms	(+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)
58.0ms	(log (+ (* re re) (* im im)))

simplify3.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5006
3	4255
2	1347
1	520
0	195

prune560.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 18.3b

localize40.0ms

Local error

Found 4 expressions with local error:

16.3b	(+ (* (* (cbrt (exp (log (sqrt (+ (* re re) (* im im)))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 60

Calls

4 calls:

111.0ms	(+ (* (* (cbrt (exp (log (sqrt (+ (* re re) (* im im)))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* (* (cbrt (exp (log (sqrt (+ (* re re) (* im im)))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
48.0ms	(sqrt (+ (* re re) (* im im)))
52.0ms	(sqrt (+ (* re re) (* im im)))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.8s

Counts

72 → 72

Iterations

Iter	Nodes
done	5003
4	3355
3	1089
2	406
1	170
0	67

prune579.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 18.3b

regimes965.0ms

Accuracy

50.6% (10.2b remaining)

Error of 26.9b against oracle of 16.8b and baseline of 37.3b

bsearch388.0ms

Steps

Iters	Range		Point
9	1.429091952413382e+57	1.929040067784495e+66	1.8791426213625292e+66
6	-2.6932251597731984e-267	-2.411444983002134e-268	-2.538815066158378e-267
8	-1.6265519976166056e-92	-7.3197477337145505e-96	-7.961223836723572e-96
8	-4.5757220010827695e-20	-1.1182933433151548e-24	-4.4945327826415316e-20
9	-2.7564489020957398e+29	-2.4929933727801765e+22	-1.0974932438808633e+26

simplify22.0ms

Iterations

Iter	Nodes
done	58
1	58
0	45

end0.0ms

sample1.9s

Algorithm

intervals

Results

553.0ms	6092×	body	80	valid
549.0ms	278×	body	5120	valid
367.0ms	657×	body	2560	valid
141.0ms	456×	body	1280	valid
108.0ms	282×	body	640	valid
59.0ms	160×	body	320	valid
9.0ms	75×	body	160	valid