Details

sample71.0ms

Algorithm

intervals

Results

54.0ms

256×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	11
1	11
0	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (sqrt (+ (* re re) (* im im))))
0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

25×	`log-pow`
24×	`times-frac`
23×	`pow1`
19×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-pow1` `pow1/2`
6×	`log-prod` `sqrt-div` `add-exp-log` `sqrt-prod` `associate-/l*`
5×	`add-cbrt-cube`
4×	`log-div` `associate-/r*`
3×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
2×	`div-sub`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `div-inv`

Counts

3 → 85

Calls

3 calls:

10.0ms	(log (sqrt (+ (* re re) (* im im))))
27.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
6.0ms	(sqrt (+ (* re re) (* im im)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(log (sqrt (+ (* re re) (* im im))))
168.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

94 → 94

Iterations

Iter	Nodes
4	2684
3	1075
2	477
1	243
0	129

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
31.3b	(log (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
82×	`add-sqr-sqrt`
54×	`sqrt-prod`
52×	`*-un-lft-identity` `add-cube-cbrt`
33×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `insert-posit16` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`frac-times` `clear-num` `frac-2neg` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 156

Calls

3 calls:

44.0ms	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
19.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
5.0ms	(log (+ (* re re) (* im im)))

series525.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
289.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
61.0ms	(log (+ (* re re) (* im im)))

simplify2.7s

Counts

165 → 165

Iterations

Iter	Nodes
3	5358
2	1703
1	549
0	208

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt 1/2) (cbrt 1/2))
1.0b	(sqrt (sqrt (log 10)))
1.0b	(sqrt (sqrt (log 10)))
31.3b	(log (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`sqrt-prod`
18×	`pow1`
17×	`*-un-lft-identity` `add-cube-cbrt`
16×	`cbrt-prod`
8×	`sqrt-pow1`
7×	`add-exp-log`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`rem-sqrt-square` `add-cbrt-cube` `pow1/2` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`log-prod` `log-pow`
2×	`log-div` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `flip3-+` `pow-plus` `rem-log-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 98

Calls

4 calls:

14.0ms	(* (cbrt 1/2) (cbrt 1/2))
3.0ms	(sqrt (sqrt (log 10)))
4.0ms	(sqrt (sqrt (log 10)))
11.0ms	(log (+ (* re re) (* im im)))

series62.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(* (cbrt 1/2) (cbrt 1/2))
0.0ms	(sqrt (sqrt (log 10)))
0.0ms	(sqrt (sqrt (log 10)))
62.0ms	(log (+ (* re re) (* im im)))

simplify2.7s

Counts

104 → 104

Iterations

Iter	Nodes
5	5740
4	1974
3	896
2	453
1	234
0	120

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

localize56.0ms

Local error

Found 4 expressions with local error:

18.5b	(log (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
12×	`pow1`
9×	`cbrt-prod` `flip3-+` `pow1/3` `log-pow` `flip-+`
8×	`log-div`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `log-prod` `pow-plus` `prod-exp`

Counts

4 → 70

Calls

4 calls:

30.0ms	(log (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(log (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
107.0ms	(cbrt (+ (* re re) (* im im)))
142.0ms	(cbrt (+ (* re re) (* im im)))
140.0ms	(cbrt (+ (* re re) (* im im)))

simplify1.9s

Counts

82 → 82

Iterations

Iter	Nodes
4	4349
3	1455
2	514
1	208
0	98

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.0b

regimes1.2s

Accuracy

57% (10.0b remaining)

Error of 17.3b against oracle of 7.2b and baseline of 30.5b

bsearch340.0ms

Steps

Iters	Range		Point
8	1.7087861021392926e+108	1.2365766446497213e+112	5.418402979673782e+109
9	-1.6476049082533209e-217	-3.0866651666303126e-226	-1.3348781049268564e-224
7	-3.6615892393549946e-147	-9.490061550273044e-149	-9.650434949786742e-149
8	-2.2544727380026611e+95	-6.663293247721072e+92	-1.388360913720003e+94

simplify38.0ms

Iterations

Iter	Nodes
2	77
1	77
0	60

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.6s

8000×

body

valid