Details

sample69.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
22.0ms	225×	body	80	nan

simplify3.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

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))
0.6b	(* (log base) (log base))
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite102.0ms

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))
12.0ms	(* (log base) (log base))
30.0ms	(sqrt (+ (* re re) (* im im)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
96.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
174.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Counts: 122 → 122

prune483.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
174.0ms	(* (log base) (log base))
174.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify167.0ms

Counts: 127 → 127

prune475.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (log base) 6))
0.6b	(* (log base) (log base))
1.3b	(pow (log base) 6)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

2.0ms	(cbrt (pow (log base) 6))
17.0ms	(* (log base) (log base))
3.0ms	(pow (log base) 6)
8.0ms	(sqrt (+ (* re re) (* im im)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (pow (log base) 6))
166.0ms	(* (log base) (log base))
208.0ms	(pow (log base) 6)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify39.0ms

Counts: 97 → 97

prune451.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.9b

localize34.0ms

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)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
9.0ms	(sqrt (+ (* re re) (* im im)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
201.0ms	(cbrt base)
205.0ms	(cbrt base)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Counts: 77 → 77

prune401.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 9.9b

regimes484.0ms

Accuracy

54.1% (11.4b remaining)

Error of 18.8b against oracle of 7.4b and baseline of 32.4b

bsearch338.0ms

Steps

Iters	Range		Point
7	5.772389280581239e+39	1.506996216864462e+41	1.4911059615158607e+41
7	-3.6236065738510993e-298	-3.7661964807787926e-300	-2.2442758803161843e-299
9	-1.0721796452230966e-175	-1.968175191369898e-182	-4.627946421707235e-181
4	-0.04521727361736504	-0.023229637516429813	-0.044279523661599256

simplify2.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	7858×	body	80	nan
999.0ms	8000×	body	80	valid