Details

sample122.0ms

Algorithm

intervals

Results

62.0ms	277×	body	80	nan
29.0ms	256×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.6b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
76.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
18.0ms	(* (log base) (log base))
17.0ms	(sqrt (+ (* re re) (* im im)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
144.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
262.0ms	(* (log base) (log base))
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Counts: 122 → 122

prune716.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
32×	`add-cube-cbrt`
31×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 130

Calls

4 calls:

72.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
20.0ms	(* (log base) (log base))
20.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
250.0ms	(* (log base) (log base))
268.0ms	(* (log base) (log base))
74.0ms	(sqrt (+ (* re re) (* im im)))

simplify142.0ms

Counts: 142 → 142

prune835.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

160.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
2.0ms	(cbrt base)
2.0ms	(cbrt base)
17.0ms	(sqrt (+ (* re re) (* im im)))

series966.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
358.0ms	(cbrt base)
281.0ms	(cbrt base)
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify37.0ms

Counts: 80 → 80

prune815.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 5.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (pow (/ 1 base) -1/3)))) (* 0.0 0.0)))
0.6b	(cbrt base)
5.2b	(pow (/ 1 base) -1/3)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
13×	`unpow-prod-down`
11×	`add-exp-log`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`pow-exp` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `pow-pow` `flip3-+` `div-exp` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-div` `associate-/r/` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `1-exp` `clear-num` `inv-pow` `sqr-pow`

Counts

4 → 89

Calls

4 calls:

150.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (pow (/ 1 base) -1/3)))) (* 0.0 0.0)))
1.0ms	(cbrt base)
17.0ms	(pow (/ 1 base) -1/3)
9.0ms	(sqrt (+ (* re re) (* im im)))

series1.3s

Counts

4 → 12

Calls

4 calls:

736.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (pow (/ 1 base) -1/3)))) (* 0.0 0.0)))
290.0ms	(cbrt base)
254.0ms	(pow (/ 1 base) -1/3)
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify81.0ms

Counts: 101 → 101

prune882.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.8b

regimes1.0s

bsearch704.0ms

Steps

Iters	Range		Point
10	1.6558114091021875e+84	3.809265903266752e+94	1.3993086544526434e+89
7	4.984156002397002e-295	1.3723675561621918e-293	5.205364392060937e-295
9	-4.911683430480342e-180	-8.55310128042087e-189	-3.060211528908098e-187
10	-5.669640616667787e+83	-2.5792957900424365e+73	-1.0085993896392872e+76

Details

sample122.0ms

simplify2.0ms

prune7.0ms

localize47.0ms

rewrite139.0ms

series601.0ms

simplify51.0ms

prune716.0ms

localize26.0ms

rewrite130.0ms

series667.0ms

simplify142.0ms

prune835.0ms

localize55.0ms

rewrite183.0ms

series966.0ms

simplify37.0ms

prune815.0ms

localize44.0ms

rewrite180.0ms

series1.3s

simplify81.0ms

prune882.0ms

regimes1.0s

bsearch704.0ms

simplify36.0ms