Details

sample91.0ms

Algorithm

intervals

Results

30.0ms	262×	body	80	nan
28.0ms	256×	body	80	valid

simplify28.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite105.0ms

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:

62.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
16.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
11.0ms	(* (log base) (log base))
13.0ms	(sqrt (+ (* re re) (* im im)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
147.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
245.0ms	(* (log base) (log base))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify864.0ms

Counts: 122 → 122

prune709.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.7b

localize33.0ms

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)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
163×	`add-sqr-sqrt`
162×	`*-un-lft-identity`
158×	`add-cube-cbrt`
141×	`sqrt-prod`
31×	`pow1`
24×	`associate-/l*`
18×	`sqrt-div`
16×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`log-prod` `swap-sqr` `log-pow`
9×	`flip3-+` `flip-+`
8×	`associate-r` `associate-l` `div-inv`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 278

Calls

4 calls:

102.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
16.0ms	(* (log base) (log base))
18.0ms	(* (log base) (log base))
24.0ms	(sqrt (+ (* re re) (* im im)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
234.0ms	(* (log base) (log base))
227.0ms	(* (log base) (log base))
70.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts: 290 → 290

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

67.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
24.0ms	(* (log base) (log base))
4.0ms	(pow (log base) 4)
12.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
538.0ms	(* (log base) (log base))
238.0ms	(pow (log base) 4)
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify927.0ms

Counts: 112 → 112

prune721.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
58×	`times-frac`
53×	`*-un-lft-identity`
43×	`add-cube-cbrt`
33×	`pow1`
32×	`associate-r` `associate-l` `sqrt-prod`
30×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`prod-exp`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `un-div-inv`

Counts

4 → 175

Calls

4 calls:

115.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
10.0ms	(* (log base) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
218.0ms	(* (log base) (log base))
183.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts: 187 → 187

prune773.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 4.6b

regimes494.0ms

Accuracy

56.5% (10.7b remaining)

Error of 18.0b against oracle of 7.3b and baseline of 32.0b

bsearch352.0ms

Steps

Iters	Range		Point
10	4.4948069819736245e+45	8.097265706245217e+58	6.261598578150243e+58
11	-4.6552436806590614e+45	-6.4619692632013955e+25	-1.3180440993817725e+42

simplify2.0s

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.3s	7981×	body	80	nan