Details

sample151.0ms

Algorithm

intervals

Results

73.0ms	256×	body	80	valid
56.0ms	250×	body	80	nan

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	22
1	22
0	18

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite65.0ms

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` `insert-posit16` `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 → 104

Calls

4 calls:

17.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
12.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
23.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
122.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
215.0ms	(* (log base) (log base))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify8.6s

Counts

116 → 116

Iterations

Iter	Nodes
3	11790
2	1707
1	417
0	162

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (/ 1 (* (log base) (log base))))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite93.0ms

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` `insert-posit16` `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 → 123

Calls

4 calls:

56.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (/ 1 (* (log base) (log base))))
18.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
11.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (/ 1 (* (log base) (log base))))
140.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
198.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.1s

Counts

135 → 135

Iterations

Iter	Nodes
3	7416
2	1498
1	500
0	195

prune1.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.8b

localize39.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ 1 (log base))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`times-frac`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
16×	`pow1` `associate-r` `add-exp-log`
10×	`add-cbrt-cube` `log-pow`
6×	`associate-l`
4×	`associate-/r*` `div-exp` `prod-exp`
3×	`sqrt-prod` `insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `flip3-+` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `flip-+` `pow-flip` `inv-pow`

Counts

3 → 95

Calls

3 calls:

7.0ms	(/ 1 (log base))
31.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
11.0ms	(sqrt (+ (* re re) (* im im)))

series387.0ms

Counts

3 → 9

Calls

3 calls:

210.0ms	(/ 1 (log base))
133.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

104 → 104

Iterations

Iter	Nodes
3	2001
2	948
1	316
0	142

prune1.1s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 7.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
0.6b	(cbrt (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
8×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`pow2` `pow-plus` `sqrt-div` `pow3` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `rem-cbrt-cube` `flip-+`

Counts

4 → 101

Calls

4 calls:

9.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
104.0ms	(cbrt (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))
7.0ms	(sqrt (+ (* re re) (* im im)))

series675.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (log base) (log base))
237.0ms	(* (log base) (log base))
215.0ms	(cbrt (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

113 → 113

Iterations

Iter	Nodes
4	2304
3	994
2	492
1	224
0	101

prune1.5s

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 7.8b

regimes498.0ms

Accuracy

59.9% (9.3b remaining)

Error of 16.7b against oracle of 7.4b and baseline of 30.5b

bsearch586.0ms

Steps

Iters	Range		Point
11	6.922539074155572e+44	2.848135779989152e+65	2.812956885343136e+65
6	3.625101584064692e-292	3.106889889053126e-291	3.674093895449681e-292
8	-1.5258001075508408e-249	-1.0455116495078457e-252	-3.1320614430937276e-251
8	-1.244212200499966e+125	-1.9586882131667533e+122	-3.6968101048126143e+124

simplify17.0ms

Iterations

Iter	Nodes
4	45
3	45
2	44
1	42
0	37

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.3s	7969×	body	80	nan
2.2s	8000×	body	80	valid