Details

sample116.0ms

Algorithm

intervals

Results

14.0ms	197×	body	80	valid
7.0ms	19×	body	2560	valid
6.0ms	14×	body	5120	valid
5.0ms	15×	body	1280	valid
1.0ms	5×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	17	15
2	24	15
3	30	15
4	35	15
done	35	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
0.8b	(- (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

54.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
17.0ms	(+ (* re re) (* im im))
64.0ms	(- (sqrt (+ (* re re) (* im im))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
33.0ms	(+ (* re re) (* im im))
67.0ms	(- (sqrt (+ (* re re) (* im im))) re)
91.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

66 → 66

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	114	942
1	255	828
2	709	752
3	2136	727
done	5000	721

prune293.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.8b	(- (sqrt (+ (* re re) (* im im))) re)
4.6b	(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `log-prod` `exp-sum`
5×	`sqrt-prod`
4×	`add-exp-log` `exp-prod` `add-cbrt-cube` `difference-of-squares`
2×	`log-div` `flip3--` `flip3-+` `exp-diff` `sqrt-div` `flip--` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `sum-log` `log-pow` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
43.0ms	(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* re re) (* im im))
69.0ms	(- (sqrt (+ (* re re) (* im im))) re)
66.0ms	(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.3s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	108	1062
1	209	917
2	504	815
3	1320	799
4	3761	789
done	5000	789

prune325.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
27.6b	(sqrt (* 2.0 (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
32×	`sqrt-prod`
28×	`times-frac`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
11×	`pow1`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`sqrt-pow1` `sqrt-div` `associate-/l*`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 93

Calls

4 calls:

88.0ms	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
71.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
24.0ms	(sqrt (* 2.0 (* im im)))
18.0ms	(sqrt (+ (* re re) (* im im)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
80.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
62.0ms	(sqrt (* 2.0 (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

105 → 105

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	181	2231
1	387	1998
2	1067	1907
3	3181	1877
done	5000	1871

prune491.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
46×	`times-frac`
39×	`sqrt-prod`
37×	`add-cube-cbrt`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1` `associate-/r*`
6×	`sqrt-div` `associate-l` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 125

Calls

4 calls:

76.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
150.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
37.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
9.0ms	(sqrt (+ (* re re) (* im im)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
215.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
60.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
55.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

137 → 137

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	248	2920
1	598	2628
2	2009	2460
done	5000	2407

prune647.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.7b

regimes354.0ms

Accuracy

53.3% (13.9b remaining)

Error of 21.8b against oracle of 7.9b and baseline of 37.6b

bsearch207.0ms

Steps

Iters	Range		Point
8	6.45163313554832e+142	6.448728304985817e+146	2.882344103991638e+143
9	-8.73589310888489e-204	-1.3616477663356908e-209	-8.615973159790101e-204

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	47
1	42	47
done	42	47

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	6047×	body	80	valid
325.0ms	655×	body	2560	valid
305.0ms	286×	body	5120	valid
167.0ms	495×	body	1280	valid
76.0ms	278×	body	640	valid
62.0ms	144×	body	320	valid
13.0ms	95×	body	160	valid