Details

sample84.0ms

Algorithm

intervals

Results

33.0ms	307×	body	80	nan
26.0ms	256×	body	80	valid

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (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))
26.9b	(sqrt (+ (* re re) (* im im)))

rewrite62.0ms

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×	`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 → 110

Calls

4 calls:

11.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
34.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
149.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
216.0ms	(* (log base) (log base))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	2906
1	507
0	200

prune992.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
26.9b	(sqrt (+ (* re re) (* im im)))

rewrite78.0ms

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×	`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 → 110

Calls

4 calls:

28.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
30.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
109.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
257.0ms	(* (log base) (log base))
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	2905
1	513
0	200

prune968.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.9b

localize83.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
26.9b	(sqrt (+ (* re re) (* im im)))
26.9b	(sqrt (+ (* re re) (* im im)))
26.9b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

5.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
64.0ms	(sqrt (+ (* re re) (* im im)))
53.0ms	(sqrt (+ (* re re) (* im im)))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	2540
2	492
1	155
0	70

prune765.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
26.9b	(sqrt (+ (* re re) (* im im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

12.0ms	(* (log base) (log base))
11.0ms	(* (log base) (log base))
11.0ms	(* (log base) (log base))
10.0ms	(sqrt (+ (* re re) (* im im)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* (log base) (log base))
213.0ms	(* (log base) (log base))
224.0ms	(* (log base) (log base))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify992.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1287
1	220
0	89

prune816.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 6.9b

regimes1.1s

Accuracy

57% (10.6b remaining)

Error of 18.0b against oracle of 7.4b and baseline of 32.2b

bsearch804.0ms

Steps

Iters	Range		Point
10	2.0355654659812002e+86	1.9878091340946106e+99	3.605929673185673e+96
9	7.967336469423699e-186	8.991875810502875e-177	8.183197557056351e-186
10	1.307026788757451e-209	1.3414481122884362e-198	9.686064739606019e-199
7	-4.079118208520745e+115	-1.823310350303199e+114	-2.195715110017203e+114

simplify24.0ms

Iterations

Iter	Nodes
done	79
3	79
2	74
1	62
0	46

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.2s	7995×	body	80	nan