Details

sample101.0ms

Algorithm

intervals

Results

26.0ms	189×	body	80	valid
22.0ms	11×	body	5120	valid
21.0ms	24×	body	2560	valid
9.0ms	13×	body	1280	valid
6.0ms	10×	body	640	valid
3.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify45.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

45.0ms

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize28.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (hypot re im) re)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

Slowest

16.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series363.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

291.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
72.0ms	(+ (hypot re im) re)

simplify554.0ms

Counts

15 → 40

Calls

15 calls:

Slowest

240.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
213.0ms	(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
29.0ms	(* (+ (hypot re im) re) 2.0)
19.0ms	(* (exp (hypot re im)) (exp re))
16.0ms	(* (+ (hypot re im) re) 2.0)

prune349.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.7b

localize34.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (hypot re im) re)
0.3b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `sqrt-prod`
7×	`associate-l` `add-cube-cbrt`
6×	`pow1` `associate-r`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `unswap-sqr`
3×	`fma-def` `pow-prod-down`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `associate-*l/` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 54

Calls

2 calls:

Slowest

34.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
9.0ms	(+ (hypot re im) re)

series338.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

250.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
88.0ms	(+ (hypot re im) re)

simplify1.3s

Counts

39 → 60

Calls

39 calls:

Slowest

439.0ms	(* (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
344.0ms	(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))
146.0ms	(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
28.0ms	(* (+ (hypot re im) re) 2.0)
23.0ms	(* (+ (hypot re im) re) 2.0)

prune634.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (hypot re im) re)
0.7b	(+ (hypot re im) re)
0.4b	(* (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))) (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))))
0.2b	(* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

81×	`pow1`
72×	`sqrt-pow1`
58×	`pow-prod-down`
38×	`sqrt-prod`
36×	`pow1/2`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
16×	`associate-*l/`
12×	`pow-prod-up` `add-cube-cbrt`
11×	`associate-l`
10×	`associate-r`
9×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
8×	`pow-sqr` `add-log-exp`
6×	`fma-def` `sqrt-unprod`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out`
2×	`+-commutative` `sum-log` `pow-plus` `associate-r/` `-commutative`
1×	`pow2` `rem-square-sqrt` `swap-sqr`

Counts

4 → 148

Calls

4 calls:

Slowest

115.0ms	(* (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))) (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))))
22.0ms	(* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))
9.0ms	(+ (hypot re im) re)
5.0ms	(+ (hypot re im) re)

series714.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

326.0ms	(* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))
244.0ms	(* (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))) (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))))
75.0ms	(+ (hypot re im) re)
69.0ms	(+ (hypot re im) re)

simplify8.0s

Counts

149 → 160

Calls

149 calls:

Slowest

544.0ms	(* (* (* (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))) (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))) (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))) (* (* (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))) (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))) (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))))
461.0ms	(* (* (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt (+ (hypot re im) re)))) (sqrt (sqrt (+ (hypot re im) re)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
457.0ms	(* (sqrt (sqrt 2.0)) (exp (* 1/4 (- (log 2) (log (/ 1 re))))))
400.0ms	(* (* (sqrt (sqrt (+ (pow (hypot re im) 3) (pow re 3)))) (sqrt (sqrt 2.0))) (* (sqrt (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0))))
377.0ms	(* (sqrt (sqrt (+ (pow (hypot re im) 3) (pow re 3)))) (sqrt (sqrt 2.0)))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.7b

localize69.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (hypot re im) re)
0.7b	(+ (hypot re im) re)
0.7b	(+ (hypot re im) re)
0.7b	(+ (hypot re im) re)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`fma-def` `add-log-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`

Counts

4 → 72

Calls

4 calls:

Slowest

5.0ms	(+ (hypot re im) re)
5.0ms	(+ (hypot re im) re)
5.0ms	(+ (hypot re im) re)
5.0ms	(+ (hypot re im) re)

series378.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

105.0ms	(+ (hypot re im) re)
100.0ms	(+ (hypot re im) re)
88.0ms	(+ (hypot re im) re)
84.0ms	(+ (hypot re im) re)

simplify174.0ms

Counts

28 → 84

Calls

28 calls:

Slowest

20.0ms	(* (exp (hypot re im)) (exp re))
16.0ms	(* (exp (hypot re im)) (exp re))
16.0ms	(* (exp (hypot re im)) (exp re))
8.0ms	(* (exp (hypot re im)) (exp re))
7.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.7b

regimes1.0s

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.3b and baseline of 13.5b

bsearch1.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	6004×	body	80	valid
511.0ms	687×	body	2560	valid
299.0ms	494×	body	1280	valid
226.0ms	284×	body	5120	valid
190.0ms	306×	body	640	valid
75.0ms	136×	body	320	valid
52.0ms	89×	body	160	valid