Details

sample78.0ms

Algorithm

intervals

Results

31.0ms	256×	body	80	valid
23.0ms	255×	body	80	nan

simplify18.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize23.0ms

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)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite156.0ms

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:

76.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
34.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
34.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
175.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
248.0ms	(* (log base) (log base))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify935.0ms

Counts: 122 → 122

prune675.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.5b

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)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite95.0ms

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:

47.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
18.0ms	(* (log base) (log base))
17.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
251.0ms	(* (log base) (log base))
224.0ms	(* (log base) (log base))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify726.0ms

Counts: 142 → 142

prune687.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.3b

localize51.0ms

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))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite107.0ms

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:

66.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
11.0ms	(* (log base) (log base))
18.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
273.0ms	(* (log base) (log base))
273.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify586.0ms

Counts: 142 → 142

prune867.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 8.2b

localize38.0ms

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)
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite124.0ms

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:

81.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
19.0ms	(* (log base) (log base))
6.0ms	(pow (log base) 4)
14.0ms	(sqrt (+ (* re re) (* im im)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
233.0ms	(* (log base) (log base))
257.0ms	(pow (log base) 4)
54.0ms	(sqrt (+ (* re re) (* im im)))

simplify777.0ms

Counts: 112 → 112

prune589.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.2b

regimes1.0s

Accuracy

57.5% (10.3b remaining)

Error of 17.5b against oracle of 7.1b and baseline of 31.4b

bsearch135.0ms

Steps

Iters	Range		Point
6	7.187788631990609e+46	3.0009874991234648e+47	2.971459169907414e+47
4	-6.138062030102188e+35	-4.090690798808291e+35	-6.074081679124254e+35

simplify74.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.2s	8127×	body	80	nan