Details

sample131.0ms

Algorithm

intervals

Results

49.0ms	256×	body	80	valid
43.0ms	305×	body	80	nan

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite115.0ms

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))
45.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
39.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
109.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
172.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts

122 → 122

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1344	2035
3	4400	1998
done	5000	1992

prune563.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
0.5b	(/ (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`pow1`
18×	`log-prod`
10×	`add-exp-log` `associate-r` `log-pow` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `sqrt-prod`
8×	`associate-l`
6×	`swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `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 → 116

Calls

4 calls:

28.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
62.0ms	(/ (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
11.0ms	(sqrt (+ (* re re) (* im im)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
160.0ms	(/ (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
225.0ms	(* (log base) (log base))
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.6s

Counts

128 → 128

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	213	2682
1	456	2354
2	1425	2134
3	4866	2109
done	5001	2103

prune652.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log base) (log (sqrt (+ (* re re) (* im im))))) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

179.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log base) (log (sqrt (+ (* re re) (* im im))))) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
10.0ms	(sqrt (+ (* re re) (* im im)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log base) (log (sqrt (+ (* re re) (* im im))))) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
190.0ms	(pow (log base) 2)
260.0ms	(pow (log base) 2)
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

152 → 152

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	235	5236
1	624	4890
2	2094	4097
done	5001	4080

prune768.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
0.4b	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
0.5b	(pow (log base) 2)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt` `associate-r`
16×	`add-exp-log`
14×	`pow1`
12×	`log-prod`
11×	`times-frac` `add-cbrt-cube`
9×	`sqrt-prod`
7×	`associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`prod-exp` `log-pow`
4×	`unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `cbrt-unprod`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-pow` `1-exp` `associate-*r/` `pow-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

128.0ms	(* (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
45.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
5.0ms	(pow (log base) 2)
14.0ms	(sqrt (+ (* re re) (* im im)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
144.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
176.0ms	(pow (log base) 2)
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

122 → 122

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	235	2811
1	561	2438
2	1811	2171
done	5000	2158

prune576.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

regimes531.0ms

Accuracy

58.8% (10.2b remaining)

Error of 17.5b against oracle of 7.3b and baseline of 32.0b

bsearch235.0ms

Steps

Iters	Range		Point
9	9.20494146023971e+137	2.5400712297185524e+145	5.033574048961893e+141
8	-2.7069606924754535e+112	-1.9215371086303872e+109	-2.0580322655456806e+110

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	40	90
1	50	88
2	53	88
done	53	88

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	8062×	body	80	nan
1.1s	8000×	body	80	valid