Details

sample112.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
34.0ms	255×	body	80	nan

simplify18.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize31.0ms

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) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite98.0ms

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:

43.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
26.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
103.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
215.0ms	(* (log base) (log base))
62.0ms	(sqrt (+ (* re re) (* im im)))

simplify861.0ms

Counts: 122 → 122

prune646.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize55.0ms

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)))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite513.0ms

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:

468.0ms	(* (/ 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)))))
10.0ms	(* (log base) (log base))
20.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (/ 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)))))
236.0ms	(* (log base) (log base))
244.0ms	(* (log base) (log base))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts: 186 → 186

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

15.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
210.0ms	(cbrt base)
263.0ms	(cbrt base)
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts: 77 → 77

prune627.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
29.0b	(sqrt (+ (* re re) (* im im)))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt base)
1.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(cbrt base)
288.0ms	(cbrt base)
42.0ms	(sqrt (+ (* re re) (* im im)))
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts: 64 → 64

prune645.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 7.0b

regimes549.0ms

Accuracy

58.4% (10.1b remaining)

Error of 17.7b against oracle of 7.6b and baseline of 32.0b

bsearch407.0ms

Steps

Iters	Range		Point
10	7.952590955742698e+105	1.0267056547773171e+120	1.4913088526759004e+116
7	1.5518954834203268e-223	2.9397084142510984e-221	6.204032340478081e-222
7	-4.866383572621146e-276	-1.413747557453483e-277	-2.1547302965462612e-277
8	-9.283390156959527e+84	-1.4426520163888441e+82	-3.2088815727908577e+84

simplify2.0s

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.4s	7645×	body	80	nan