Details

sample153.0ms

Algorithm

intervals

Results

57.0ms	256×	body	80	valid
51.0ms	281×	body	80	nan

simplify31.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize48.0ms

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))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite143.0ms

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:

16.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
59.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
43.0ms	(* (log base) (log base))
17.0ms	(sqrt (+ (* re re) (* im im)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
143.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
253.0ms	(* (log base) (log base))
69.0ms	(sqrt (+ (* re re) (* im im)))

simplify956.0ms

Counts: 122 → 122

prune693.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (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))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite223.0ms

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/`

Counts

4 → 174

Calls

4 calls:

155.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
30.0ms	(* (log base) (log base))
11.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
219.0ms	(* (log base) (log base))
203.0ms	(* (log base) (log base))
76.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts: 186 → 186

prune917.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
0.6b	(pow (log base) 2)
0.6b	(* (log base) (log base))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
58×	`times-frac`
47×	`*-un-lft-identity`
39×	`add-cube-cbrt`
32×	`sqrt-prod`
29×	`add-exp-log`
28×	`associate-r` `associate-l`
22×	`pow1`
18×	`add-cbrt-cube`
16×	`unswap-sqr`
9×	`prod-exp`
8×	`div-exp`
7×	`log-pow`
6×	`log-prod` `sqrt-div` `swap-sqr`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `unpow-prod-down` `associate-/r/` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `flip-+`
2×	`rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`pow2` `frac-times` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `associate-l/` `pow-exp` `pow-sqr` `pow-prod-up` `unpow2` `sqr-pow`

Counts

4 → 157

Calls

4 calls:

124.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
4.0ms	(pow (log base) 2)
11.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
172.0ms	(pow (log base) 2)
172.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts: 169 → 169

prune1.0s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
0.8b	(pow (* (log base) (log base)) 3)
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow1`
23×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `pow-pow` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow2` `pow-unpow` `pow-plus` `pow-prod-down` `prod-exp` `sqrt-prod` `pow-sqr` `pow-prod-up` `cbrt-unprod`
2×	`sqrt-div` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `cube-prod` `flip-+` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

19.0ms	(* (log base) (log base))
11.0ms	(* (log base) (log base))
8.0ms	(pow (* (log base) (log base)) 3)
9.0ms	(sqrt (+ (* re re) (* im im)))

series921.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (log base) (log base))
471.0ms	(* (log base) (log base))
205.0ms	(pow (* (log base) (log base)) 3)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify462.0ms

Counts: 125 → 125

prune956.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.2b

regimes861.0ms

Accuracy

57% (10.5b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 31.9b

bsearch624.0ms

Steps

Iters	Range		Point
8	9.700072250313438e+141	5.436846249801555e+146	1.2303366234451559e+145
11	1.9195236113751486e-181	3.5787809254959396e-148	1.7918307825710592e-180
8	-3.5414651521624704e-184	-9.889531392243277e-188	-1.607695456247534e-186
10	-7.065909207097609e+129	-9.010206292018322e+112	-1.4702290859562654e+113

simplify1.8s

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.2s	8204×	body	80	nan