Details

sample404.0ms

Algorithm

intervals

Results

35.0ms	190×	body	80	valid
17.0ms	22×	body	1280	valid
15.0ms	17×	body	2560	valid
10.0ms	7×	body	5120	valid
6.0ms	10×	body	640	valid
4.0ms	8×	body	320	valid
1.0ms	2×	body	160	valid

simplify516.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

515.0ms

(* 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: 14.8b

localize16.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (hypot re im) re)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))

rewrite25.0ms

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)

series340.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

256.0ms	(sqrt (* (- (hypot re im) re) 2.0))
84.0ms	(- (hypot re im) re)

simplify1.1s

Counts

35 → 51

Calls

35 calls:

Slowest

254.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
174.0ms	(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
71.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))
56.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
55.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))

prune588.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.6b

localize35.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (hypot re im) re)
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`sqrt-prod`
9×	`prod-diff`
8×	`associate-l`
6×	`pow1` `associate-r`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `unswap-sqr`
3×	`fma-neg` `pow-prod-down`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `associate-*l/` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 66

Calls

2 calls:

Slowest

39.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
10.0ms	(- (hypot re im) re)

series315.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

233.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
83.0ms	(- (hypot re im) re)

simplify1.6s

Counts

60 → 72

Calls

60 calls:

Slowest

333.0ms	(* (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
213.0ms	(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
201.0ms	(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))
73.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
50.0ms	(* (- (hypot re im) re) 2.0)

prune686.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 14.6b

localize40.0ms

Local error

Found 4 expressions with local error:

16.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 57

Calls

4 calls:

Slowest

4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series808.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

344.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
175.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
156.0ms	(sqrt (hypot re im))
133.0ms	(sqrt (hypot re im))

simplify141.0ms

Counts

25 → 69

Calls

25 calls:

Slowest

45.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
35.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
15.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
6.0ms	(sqrt (sqrt (hypot re im)))
5.0ms	(sqrt (hypot re im))

prune722.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.5b

localize27.0ms

Local error

Found 4 expressions with local error:

9.0b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr` `add-log-exp`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `sum-log`
1×	`pow2` `neg-sub0` `+-commutative` `associate-+r-` `rem-square-sqrt` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `unsub-neg` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 103

Calls

4 calls:

Slowest

21.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
2.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (hypot re im))

series352.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

112.0ms	(sqrt (hypot re im))
102.0ms	(sqrt (hypot re im))
70.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
68.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.2s

Counts

84 → 115

Calls

84 calls:

Slowest

238.0ms	(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp (- re)))
218.0ms	(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (/ 1 (exp re)))
163.0ms	(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
96.0ms	(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
23.0ms	(+ 1/2 (/ 1 2))

prune1.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 14.5b

regimes331.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch1.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	5955×	body	80	valid
642.0ms	727×	body	2560	valid
313.0ms	494×	body	1280	valid
266.0ms	312×	body	5120	valid
216.0ms	285×	body	640	valid
53.0ms	148×	body	320	valid
37.0ms	79×	body	160	valid