Details

sample199.0ms

Algorithm

intervals

Results

33.0ms	195×	body	80	valid
19.0ms	20×	body	2560	valid
13.0ms	18×	body	1280	valid
6.0ms	9×	body	640	valid
5.0ms	5×	body	5120	valid
3.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify97.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

97.0ms

(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (hypot re im) re)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 45

Calls

2 calls:

Slowest

8.0ms	(sqrt (* (- (hypot re im) re) 2.0))
7.0ms	(- (hypot re im) re)

series326.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

231.0ms	(sqrt (* (- (hypot re im) re) 2.0))
94.0ms	(- (hypot re im) re)

simplify1.1s

Counts

35 → 51

Calls

35 calls:

Slowest

293.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
167.0ms	(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
48.0ms	(* (- (hypot re im) re) 2.0)
47.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
45.0ms	(* (- (hypot re im) re) 2.0)

prune387.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (hypot re im) re)
0.8b	(- (hypot re im) re)
0.8b	(- (hypot re im) re)
0.4b	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`cbrt-prod`
27×	`prod-diff`
12×	`cbrt-div`
11×	`pow1`
10×	`swap-sqr` `add-log-exp`
9×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`pow1/3` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 146

Calls

4 calls:

Slowest

48.0ms	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
10.0ms	(- (hypot re im) re)
10.0ms	(- (hypot re im) re)
9.0ms	(- (hypot re im) re)

series509.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

204.0ms	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
109.0ms	(- (hypot re im) re)
107.0ms	(- (hypot re im) re)
88.0ms	(- (hypot re im) re)

simplify4.9s

Counts

152 → 158

Calls

152 calls:

Slowest

350.0ms	(- (+ (pow im 2/3) (* 2/9 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3)))) (* 2/3 (* re (pow (/ 1 im) 1/3))))
333.0ms	(* (cbrt (- (* (hypot re im) (hypot re im)) (* re re))) (cbrt (- (pow (hypot re im) 3) (pow re 3))))
269.0ms	(* (cbrt (- (pow (hypot re im) 3) (pow re 3))) (cbrt (- (* (hypot re im) (hypot re im)) (* re re))))
264.0ms	(* (cbrt (- (* (hypot re im) (hypot re im)) (* re re))) (cbrt (- (hypot re im) re)))
257.0ms	(exp (* 1/3 (- (log 4) (* 2 (log (/ -1 re))))))

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.4b

localize46.0ms

Local error

Found 4 expressions with local error:

14.7b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
0.8b	(- (hypot re im) re)
0.8b	(- (hypot re im) re)
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
16×	`cbrt-prod`
11×	`pow1`
8×	`add-log-exp`
6×	`fma-neg` `pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 112

Calls

4 calls:

Slowest

15.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
10.0ms	(- (hypot re im) re)
9.0ms	(- (hypot re im) re)
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series582.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

222.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
171.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
105.0ms	(- (hypot re im) re)
84.0ms	(- (hypot re im) re)

simplify1.6s

Counts

104 → 124

Calls

104 calls:

Slowest

127.0ms	(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))
89.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
79.0ms	(* (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))) (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))))
68.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))
53.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.4b

localize84.0ms

Local error

Found 4 expressions with local error:

14.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
14.7b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
0.8b	(- (hypot re im) re)
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
16×	`cbrt-prod`
11×	`pow1`
9×	`prod-diff`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `fma-udef`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 94

Calls

4 calls:

Slowest

8.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
5.0ms	(- (hypot re im) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series659.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

203.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
191.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
171.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
94.0ms	(- (hypot re im) re)

simplify1.1s

Counts

80 → 106

Calls

80 calls:

Slowest

137.0ms	(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))
72.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
66.0ms	(* (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))) (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))))
52.0ms	(fma 1 (hypot re im) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
51.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.4b

regimes573.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch2.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

722.0ms	457×	body	1280	valid
695.0ms	6087×	body	80	valid
548.0ms	663×	body	2560	valid
383.0ms	286×	body	5120	valid
152.0ms	285×	body	640	valid
45.0ms	139×	body	320	valid
16.0ms	83×	body	160	valid