Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	191×	body	80	valid
4.0ms	24×	body	2560	valid
2.0ms	15×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	6×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8
done	24	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

30.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series87.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Counts

33 → 33

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	141	198
1	358	186
2	866	182
3	2557	181
4	5001	181
done	5001	181

prune104.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.3b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
31.7b	(sqrt (+ (* re re) (* im im)))
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
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×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

50.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
29.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
49.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950
done	5001	950

prune285.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
13.4b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
31.7b	(sqrt (+ (* re re) (* im im)))
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

13.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
33.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
50.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	394	992
1	1342	878
2	5001	845
done	5001	845

prune320.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.2b

localize19.0ms

Local error

Found 4 expressions with local error:

11.9b	(+ (* (* (sqrt (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)) (sqrt (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3))) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
31.7b	(sqrt (+ (* re re) (* im im)))
31.7b	(sqrt (+ (* re re) (* im im)))
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

151.0ms	(+ (* (* (sqrt (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)) (sqrt (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3))) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* (* (sqrt (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)) (sqrt (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3))) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
42.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify82.0ms

Counts

68 → 68

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	170	720
1	558	621
2	2165	604
3	5002	603
done	5002	603

prune333.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

regimes172.0ms

Accuracy

57.1% (9.9b remaining)

Error of 27.4b against oracle of 17.5b and baseline of 40.6b

bsearch126.0ms

Steps

Iters	Range	Point
9	1.596161804377022e+119	4.919965018933925e+124	2.0656519016176576e+119
10	2.7636474607770915e-218	1.3181567757377188e-202	2.165263052480363e-217
7	-1.1247036883386809e-263	-5.3645173288875583e-266	-1.0158325814464316e-264

Iters

Range

Point

1.596161804377022e+119

4.919965018933925e+124

2.0656519016176576e+119

2.7636474607770915e-218

1.3181567757377188e-202

2.165263052480363e-217

-1.1247036883386809e-263

-5.3645173288875583e-266

-1.0158325814464316e-264

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	37
1	63	37
2	63	37
done	63	37

end0.0ms

sample686.0ms

Algorithm

intervals

Results

188.0ms	6052×	body	80	valid
134.0ms	720×	body	2560	valid
69.0ms	445×	body	1280	valid
67.0ms	273×	body	5120	valid
35.0ms	297×	body	640	valid
17.0ms	145×	body	320	valid
4.0ms	68×	body	160	valid