Details

sample142.0ms

Algorithm

intervals

Results

54.0ms	305×	body	80	nan
43.0ms	256×	body	80	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize38.0ms

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)))

rewrite141.0ms

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:

25.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
91.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
12.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
155.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
246.0ms	(* (log base) (log base))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify8.8s

Counts

122 → 122

Iterations

Useful iterations: done (8.8s)

Iter	Nodes	Cost
0	200	2451
done	5000	2228

prune810.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite276.0ms

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:

244.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
4.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
9.0ms	(sqrt (+ (* re re) (* im im)))

series775.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
268.0ms	(pow (log base) 2)
230.0ms	(pow (log base) 2)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify937.0ms

Counts

152 → 152

Iterations

Useful iterations: done (928.0ms)

Iter	Nodes	Cost
0	235	5236
done	5000	4880

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
1.0b	(pow (log base) (* 2 2))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`unpow-prod-down`
11×	`pow1` `add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log` `pow-unpow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `sqrt-prod` `log-pow` `sqr-pow`
2×	`sqrt-div` `unpow2`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 69

Calls

4 calls:

3.0ms	(pow (log base) 2)
4.0ms	(pow (log base) 2)
4.0ms	(pow (log base) (* 2 2))
9.0ms	(sqrt (+ (* re re) (* im im)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(pow (log base) 2)
233.0ms	(pow (log base) 2)
303.0ms	(pow (log base) (* 2 2))
75.0ms	(sqrt (+ (* re re) (* im im)))

simplify18.8s

Counts

81 → 81

Iterations

Useful iterations: done (18.7s)

Iter	Nodes	Cost
0	95	693
1	1386	527
done	5000	493

prune592.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `unpow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

6.0ms	(pow (log base) 2)
13.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(pow (log base) 2)
59.0ms	(sqrt (+ (* re re) (* im im)))
51.0ms	(sqrt (+ (* re re) (* im im)))
76.0ms	(sqrt (+ (* re re) (* im im)))

simplify12.0s

Counts

76 → 76

Iterations

Useful iterations: done (12.0s)

Iter	Nodes	Cost
0	74	788
1	866	674
done	5001	628

prune500.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 8.9b

regimes774.0ms

Accuracy

58.8% (10.1b remaining)

Error of 17.5b against oracle of 7.3b and baseline of 31.9b

bsearch318.0ms

Steps

Iters	Range		Point
9	9.20494146023971e+137	2.5400712297185524e+145	9.385054520910622e+137
9	-2.1962666116397044e+118	-2.7069606924754535e+112	-2.178124817795753e+114

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	77
1	53	77
done	53	77

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.3s	8062×	body	80	nan
1.3s	8000×	body	80	valid