Details

sample107.0ms

Algorithm

intervals

Results

50.0ms	220×	body	80	nan
39.0ms	256×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	2408
8	2408
7	1116
6	232
5	78
4	53
3	39
2	24
1	22
0	18

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`associate-/r*` `sqrt-div`
3×	`flip3-+` `sqrt-prod` `flip-+` `insert-posit16`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 77

Calls

3 calls:

14.0ms	(+ (* re re) (* im im))
28.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series245.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* re re) (* im im))
144.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

86 → 86

Iterations

Iter	Nodes
done	2007
3	2007
2	686
1	269
0	133

prune454.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(/ 1 (log base))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

10.0ms	(+ (* re re) (* im im))
4.0ms	(/ 1 (log base))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* re re) (* im im))
234.0ms	(/ 1 (log base))
133.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
61.0ms	(sqrt (+ (* re re) (* im im)))

simplify771.0ms

Counts

119 → 119

Iterations

Iter	Nodes
done	2011
3	2011
2	981
1	355
0	152

prune541.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
0.6b	(* (log base) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-cbrt-cube` `associate-l` `add-exp-log` `log-pow`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `flip3-+` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `pow-plus` `div-exp` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 114

Calls

4 calls:

10.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
38.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
17.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
108.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
184.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	2003
3	2003
2	1087
1	492
0	204

prune668.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
0.6b	(cbrt base)
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt base)
1.0ms	(cbrt base)
1.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

237.0ms	(cbrt base)
238.0ms	(cbrt base)
505.0ms	(cbrt base)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify984.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	2003
5	2003
4	1478
3	601
2	285
1	132
0	62

prune424.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.2b

regimes521.0ms

Accuracy

58.5% (9.9b remaining)

Error of 17.1b against oracle of 7.2b and baseline of 31.1b

bsearch197.0ms

Steps

Iters	Range		Point
6	1.1212857151255351e+101	4.5574133216931925e+101	1.2874468181519675e+101
10	-4.411955781697599e+102	-9.644007040214822e+85	-1.4571941010285686e+94

simplify22.0ms

Iterations

Iter	Nodes
done	48
2	48
1	47
0	37

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.1s	7811×	body	80	nan
1.8s	8000×	body	80	valid