Details

sample128.0ms

Algorithm

intervals

Results

59.0ms	256×	body	80	valid
46.0ms	230×	body	80	nan

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	22
1	22
0	18

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

17.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
125.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
225.0ms	(* (log base) (log base))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify9.0s

Counts

112 → 112

Iterations

Iter	Nodes
3	14214
2	1721
1	406
0	158

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
0.3b	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
94×	`log-pow`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
79×	`pow1`
34×	`associate-/r*`
22×	`sqrt-pow1` `pow1/2`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
4×	`cbrt-undiv`
3×	`sqrt-prod`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `sqrt-div` `1-exp` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 208

Calls

4 calls:

10.0ms	(+ (* re re) (* im im))
6.0ms	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
7.0ms	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* re re) (* im im))
180.0ms	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
175.0ms	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.2s

Counts

220 → 220

Iterations

Iter	Nodes
3	4780
2	1662
1	611
0	250

prune2.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (/ 1 (* (log base) (log base))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-exp-log`
29×	`add-cbrt-cube` `prod-exp`
28×	`pow1`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`associate-r`
13×	`cbrt-unprod`
12×	`log-prod`
11×	`associate-l`
10×	`log-pow`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
5×	`pow-prod-down`
4×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
3×	`times-frac` `*-commutative` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `flip3-+` `pow-plus` `associate-*r/` `pow-sqr` `un-div-inv` `pow-prod-up` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

50.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (/ 1 (* (log base) (log base))))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (/ 1 (* (log base) (log base))))
126.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
229.0ms	(* (log base) (log base))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify13.6s

Counts

131 → 131

Iterations

Iter	Nodes
3	9291
2	1726
1	503
0	191

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.6b

localize87.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt base)
0.5b	(cbrt base)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
6×	`cbrt-prod` `log-prod` `add-cbrt-cube` `associate-l` `add-exp-log`
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)
10.0ms	(sqrt (+ (* re re) (* im im)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
265.0ms	(cbrt base)
241.0ms	(cbrt base)
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

77 → 77

Iterations

Iter	Nodes
4	3155
3	1308
2	551
1	244
0	116

prune1.2s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 6.6b

regimes605.0ms

Accuracy

57.8% (9.9b remaining)

Error of 17.2b against oracle of 7.3b and baseline of 30.8b

bsearch565.0ms

Steps

Iters	Range		Point
9	1.4724205367214046e+117	3.6649123875674516e+124	1.0886698489818444e+124
10	9.838575980955753e-220	3.291115018037162e-207	1.7444208998420076e-211
6	-4.8825757857151075e-285	-9.495595224939356e-286	-1.361373372799871e-285
7	-2.263132015969155e+107	-4.1331456445201793e+105	-9.275512899723917e+106

simplify20.0ms

Iterations

Iter	Nodes
4	46
3	46
2	44
1	43
0	38

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.5s	8160×	body	80	nan
2.0s	8000×	body	80	valid