Details

sample56.0ms

Algorithm

intervals

Results

31.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify659.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2152
3	441
2	102
1	35
0	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize52.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

3.4b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite914.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`associate-/l/`
3×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`

Counts

3 → 453

Calls

3 calls:

292.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

363.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

246.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series565.0ms

Counts

3 → 9

Calls

3 calls:

213.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

231.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

120.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.9s

Counts

462 → 462

Iterations

Iter	Nodes
2	4067
1	1356
0	582

prune5.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize56.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

0.1b

(/ (* 1 (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

3.4b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite965.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
101×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`add-exp-log`
24×	`add-cbrt-cube`
23×	`associate-/l*`
18×	`distribute-lft-out`
17×	`div-exp`
14×	`associate-/r/`
11×	`cbrt-undiv`
10×	`associate-/r*`
8×	`flip3-+` `flip-+`
7×	`div-inv`
6×	`prod-exp`
4×	`associate-/l/`
3×	`pow1` `clear-num` `frac-2neg` `1-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
1×	`associate-*r/`

Counts

3 → 163

Calls

3 calls:

384.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

310.0ms

(/ (* 1 (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

266.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series527.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

209.0ms

(/ (* 1 (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

121.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.0s

Counts

172 → 172

Iterations

Iter	Nodes
2	2708
1	760
0	279

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
0.4b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite575.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
68×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`associate-/l*`
12×	`associate-/r*` `sqrt-div`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `insert-posit16` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 180

Calls

4 calls:

187.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
188.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
85.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
111.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series470.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
157.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
78.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
79.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify982.0ms

Counts

192 → 192

Iterations

Iter	Nodes
3	2685
2	804
1	331
0	162

prune2.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize72.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2 1))))
3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite683.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
17×	`*-un-lft-identity`
12×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`flip3-+` `flip-+`
9×	`add-exp-log`
8×	`associate-/l/`
7×	`add-cbrt-cube`
6×	`associate-/r*` `times-frac` `sqrt-prod`
4×	`frac-times` `pow1` `insert-posit16` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 83

Calls

4 calls:

135.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2 1))))
57.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
441.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series552.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2 1))))
85.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
84.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
92.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.5s

Counts

95 → 95

Iterations

Iter	Nodes
3	5664
2	1512
1	538
0	200

prune1.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes128.0ms

Accuracy

53.2% (1.2b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.6b

bsearch90.0ms

Steps

Iters	Range		Point
7	1.075388870107967e+167	5.681342417267281e+168	4.0898973557336655e+168

simplify6.0ms

Iterations

Iter	Nodes
2	28
1	28
0	20

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
313.0ms	8000×	pre	80	true