Details

sample1.1s

Algorithm

intervals

Results

791.0ms	258×	body	10240	exit
155.0ms	507×	body	80	nan
61.0ms	256×	body	80	valid

simplify136.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

136.0ms

(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (log (hypot re im)) (log base))
0.0b	(hypot re im)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`times-frac`
12×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
10×	`log-pow`
4×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `hypot-udef` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 50

Calls

2 calls:

Slowest

10.0ms	(/ (log (hypot re im)) (log base))
0.0ms	(hypot re im)

series217.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

135.0ms	(/ (log (hypot re im)) (log base))
82.0ms	(hypot re im)

simplify1.3s

Counts

46 → 56

Calls

46 calls:

Slowest

471.0ms	(/ (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (log base) (log base)) (log base)))
252.0ms	(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
70.0ms	(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) (* (cbrt (log base)) (cbrt (log base))))
39.0ms	(/ (log (/ 1 re)) (log (/ 1 base)))
38.0ms	(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) (sqrt (log base)))

prune681.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (log (hypot re im)) (/ 1 (log base)))
0.2b	(/ 1 (log base))
0.0b	(hypot re im)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`times-frac`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`associate-r` `add-exp-log`
14×	`pow1`
10×	`add-cbrt-cube`
8×	`log-pow`
4×	`associate-/r` `div-exp` `associate-l*` `prod-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 92

Calls

3 calls:

Slowest

13.0ms	(* (log (hypot re im)) (/ 1 (log base)))
4.0ms	(/ 1 (log base))
0.0ms	(hypot re im)

series480.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

257.0ms	(/ 1 (log base))
159.0ms	(* (log (hypot re im)) (/ 1 (log base)))
63.0ms	(hypot re im)

simplify2.2s

Counts

76 → 101

Calls

76 calls:

Slowest

492.0ms	(* (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base))))
360.0ms	(* (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (/ (* (* 1 1) 1) (* (* (log base) (log base)) (log base))))
153.0ms	(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
83.0ms	(+ (log (log (hypot re im))) (- 0 (log (log base))))
82.0ms	(/ (* (* 1 1) 1) (* (* (log base) (log base)) (log base)))

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

8.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series685.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
172.0ms	(cbrt (hypot re im))
154.0ms	(cbrt (hypot re im))
150.0ms	(cbrt (hypot re im))

simplify1.3s

Counts

65 → 97

Calls

65 calls:

Slowest

233.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
188.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
181.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
168.0ms	(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))
91.0ms	(* (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))) (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

5.2b	(exp (+ (log (cbrt (hypot re im))) (log (cbrt (hypot re im)))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`exp-prod`
20×	`log-pow`
18×	`pow1`
12×	`add-sqr-sqrt` `distribute-rgt-out` `add-cube-cbrt`
9×	`cbrt-prod` `pow1/3`
7×	`distribute-lft-out`
5×	`exp-to-pow` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`distribute-lft1-in` `distribute-rgt1-in` `rem-exp-log`
1×	`sum-log` `exp-sum`

Counts

4 → 81

Calls

4 calls:

Slowest

21.0ms	(exp (+ (log (cbrt (hypot re im))) (log (cbrt (hypot re im)))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series628.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

176.0ms	(exp (+ (log (cbrt (hypot re im))) (log (cbrt (hypot re im)))))
167.0ms	(cbrt (hypot re im))
145.0ms	(cbrt (hypot re im))
140.0ms	(cbrt (hypot re im))

simplify1.5s

Counts

50 → 93

Calls

50 calls:

Slowest

246.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
226.0ms	(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))
224.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
216.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
125.0ms	(exp (* (cbrt (+ (log (cbrt (hypot re im))) (log (cbrt (hypot re im))))) (cbrt (+ (log (cbrt (hypot re im))) (log (cbrt (hypot re im)))))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes440.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample36.1s

Algorithm

intervals

Results

27.9s	7978×	body	10240	exit
4.9s	15931×	body	80	nan
2.3s	8000×	body	80	valid