Details

sample73.0ms

Algorithm

intervals

Results

21.0ms	189×	body	80	valid
17.0ms	25×	body	2560	valid
9.0ms	14×	body	1280	valid
7.0ms	10×	body	5120	valid
5.0ms	11×	body	640	valid
2.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify64.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

64.0ms

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b	(+ (hypot re im) re)
0.1b	(sqrt (* (+ (hypot re im) re) 2.0))
0.0b	(* (+ (hypot re im) re) 2.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

Slowest

28.0ms	(* (+ (hypot re im) re) 2.0)
13.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
5.0ms	(+ (hypot re im) re)

series390.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

215.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
93.0ms	(+ (hypot re im) re)
82.0ms	(* (+ (hypot re im) re) 2.0)

simplify1.7s

Counts

29 → 67

Calls

29 calls:

Slowest

562.0ms	(* (+ (pow (hypot re im) 3) (pow re 3)) 2.0)
268.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
243.0ms	(* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0)
209.0ms	(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
171.0ms	(* (* (* (+ (hypot re im) re) (+ (hypot re im) re)) (+ (hypot re im) re)) (* (* 2.0 2.0) 2.0))

prune706.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.6b

localize32.0ms

Local error

Found 4 expressions with local error:

16.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.1b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0b	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
0.0b	(sqrt (hypot re im))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `pow1`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `associate-r` `associate-l`
2×	`pow1/2` `pow-prod-down`
1×	`rem-sqrt-square` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

Slowest

6.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
1.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series854.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

326.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
234.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
189.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
105.0ms	(sqrt (hypot re im))

simplify479.0ms

Counts

29 → 74

Calls

29 calls:

Slowest

274.0ms	(* (* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (* (* 2.0 2.0) 2.0))
50.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
31.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
31.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
11.0ms	(+ (* 2.0 re) (* 2.0 im))

prune782.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.6b

localize27.0ms

Local error

Found 4 expressions with local error:

16.3b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`sqrt-pow1`
31×	`pow1`
20×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 133

Calls

4 calls:

Slowest

14.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
4.0ms	(sqrt (sqrt (hypot re im)))
3.0ms	(sqrt (sqrt (hypot re im)))
0.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

series661.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

214.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)
167.0ms	(sqrt (sqrt (hypot re im)))
150.0ms	(sqrt (sqrt (hypot re im)))
129.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify1.7s

Counts

140 → 145

Calls

140 calls:

Slowest

214.0ms	(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
207.0ms	(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
147.0ms	(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))
77.0ms	(* (* (cbrt (sqrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))) (* (cbrt (sqrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))))
31.0ms	(pow (/ 1 re) -1/4)

prune1.8s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 13.6b

localize79.0ms

Local error

Found 4 expressions with local error:

16.4b	(fma (sqrt (hypot re im)) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))) (sqrt (sqrt (cbrt (hypot re im))))) re)
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

Slowest

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))) (sqrt (sqrt (cbrt (hypot re im))))) re)

series641.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

188.0ms	(fma (sqrt (hypot re im)) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))) (sqrt (sqrt (cbrt (hypot re im))))) re)
162.0ms	(cbrt (hypot re im))
159.0ms	(cbrt (hypot re im))
132.0ms	(cbrt (hypot re im))

simplify795.0ms

Counts

21 → 65

Calls

21 calls:

Slowest

217.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
211.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
161.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
37.0ms	(pow (/ 1 re) -1/3)
28.0ms	(pow (/ 1 re) -1/3)

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 13.6b

regimes325.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch3.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

879.0ms	6057×	body	80	valid
676.0ms	300×	body	5120	valid
505.0ms	651×	body	2560	valid
277.0ms	501×	body	1280	valid
186.0ms	274×	body	640	valid
50.0ms	152×	body	320	valid
15.0ms	65×	body	160	valid