Details

sample101.0ms

Algorithm

intervals

Results

13.0ms	34×	body	2560	valid
11.0ms	168×	body	80	valid
7.0ms	16×	body	5120	valid
5.0ms	17×	body	1280	valid
3.0ms	12×	body	640	valid
2.0ms	4×	body	160	valid
1.0ms	5×	body	320	valid

simplify92.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
27.3b	(sqrt (+ (* re re) (* im im)))

rewrite228.0ms

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:

59.0ms	(+ (* re re) (* im im))
46.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
109.0ms	(- (sqrt (+ (* re re) (* im im))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* re re) (* im im))
268.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
99.0ms	(- (sqrt (+ (* re re) (* im im))) re)
116.0ms	(sqrt (+ (* re re) (* im im)))

simplify896.0ms

Counts

66 → 66

Iterations

Useful iterations: done (892.0ms)

Iter	Nodes	Cost
0	114	942
1	276	836
2	1265	752
done	5000	729

prune281.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
10.6b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.3b	(sqrt (+ (* re re) (* im im)))
27.3b	(sqrt (+ (* re re) (* im im)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

64.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
60.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
64.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
68.0ms	(sqrt (+ (* re re) (* im im)))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

138 → 138

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	138	3069
1	295	1778
2	1174	1607
done	5001	1572

prune466.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.4b

localize52.0ms

Local error

Found 4 expressions with local error:

27.3b	(sqrt (+ (* re re) (* im im)))
28.3b	(cbrt (+ (* re re) (* im im)))
28.3b	(cbrt (+ (* re re) (* im im)))
28.3b	(cbrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

8.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (+ (* re re) (* im im)))
136.0ms	(cbrt (+ (* re re) (* im im)))
138.0ms	(cbrt (+ (* re re) (* im im)))
119.0ms	(cbrt (+ (* re re) (* im im)))

simplify3.1s

Counts

66 → 66

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	65	909
1	150	864
2	547	746
3	3211	737
done	5002	737

prune505.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
27.2b	(sqrt (* 2.0 (+ (* im im) 0)))
27.3b	(sqrt (+ (* re re) (* im im)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

71.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
27.0ms	(sqrt (+ (* re re) (* im im)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
65.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
50.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	198	2506
1	462	2091
2	2073	1954
done	5002	1936

prune546.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.7b

regimes375.0ms

Accuracy

66.7% (8.9b remaining)

Error of 19.2b against oracle of 10.3b and baseline of 37.1b

bsearch232.0ms

Steps

Iters	Range	Point
9	1.8332650139728974e+145	1.8449387490349621e+151	1.8194409502879773e+151
10	-3.547288156007854e-304	1.1627053065331661e-300	-2.8311881040630894e-307
6	-1.2367004894298031e+109	-1.969700704475786e+108	-1.1785944497771992e+109

Iters

Range

Point

1.8332650139728974e+145

1.8449387490349621e+151

1.8194409502879773e+151

-3.547288156007854e-304

1.1627053065331661e-300

-2.8311881040630894e-307

-1.2367004894298031e+109

-1.969700704475786e+108

-1.1785944497771992e+109

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	44	81
1	55	79
2	56	79
done	56	79

end0.0ms

sample2.4s

Algorithm

intervals

Results

687.0ms	497×	body	1280	valid
570.0ms	5920×	body	80	valid
458.0ms	741×	body	2560	valid
218.0ms	328×	body	5120	valid
77.0ms	292×	body	640	valid
27.0ms	141×	body	320	valid
10.0ms	81×	body	160	valid