Details

sample74.0ms

Algorithm

intervals

Results

23.0ms	206×	body	80	valid
12.0ms	21×	body	640	valid
9.0ms	256×	pre	80	true
6.0ms	11×	body	1280	valid
6.0ms	17×	body	320	valid
0.0ms	1×	body	160	valid

simplify847.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2042
4	2042
3	440
2	95
1	32
0	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.8b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

0.7b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

18.4b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite671.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 114

Calls

3 calls:

130.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

484.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

54.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series773.0ms

Counts

3 → 9

Calls

3 calls:

289.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

376.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

107.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify882.0ms

Counts

123 → 123

Iterations

Iter	Nodes
done	2001
2	2001
1	697
0	228

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.9b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite569.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-cbrt-cube` `add-exp-log`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-l` `insert-posit16`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/`
1×	`+-commutative` `sum-log` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 299

Calls

4 calls:

32.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
121.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
333.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
76.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
233.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
340.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
345.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.3s

Counts

311 → 311

Iterations

Iter	Nodes
done	2005
2	2005
1	1128
0	389

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
1.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.7b	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
2.9b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite633.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
134×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
90×	`associate-r`
66×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`div-inv`
4×	`log-div` `exp-prod` `associate-l` `insert-posit16`
3×	`cbrt-undiv` `div-exp` `exp-sum` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `exp-diff` `associate-*l/` `log-pow`
1×	`+-commutative` `sum-log` `rem-log-exp` `pow-prod-down` `associate-r/` `-commutative` `rem-exp-log`

Counts

4 → 163

Calls

4 calls:

76.0ms	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
361.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
92.0ms	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
100.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

371.0ms	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
309.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
420.0ms	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
429.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.3s

Counts

175 → 175

Iterations

Iter	Nodes
done	2002
2	2002
1	977
0	332

prune2.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b	(* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
0.4b	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
6.8b	(+ (* (* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

313×	`times-frac`
261×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
151×	`add-cube-cbrt`
118×	`sqrt-prod`
30×	`distribute-lft-out`
27×	`associate-r`
24×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
22×	`add-exp-log` `associate-/r/`
16×	`add-cbrt-cube`
14×	`associate-/r*` `flip3-+` `flip-+`
11×	`div-inv`
8×	`pow1`
7×	`div-exp`
6×	`sqrt-div` `add-log-exp`
5×	`cbrt-undiv` `unswap-sqr`
4×	`associate-l` `prod-exp` `insert-posit16`
3×	`pow-flip`
2×	`frac-times` `rec-exp` `clear-num` `frac-2neg` `1-exp` `div-sub` `associate-*l/` `cbrt-unprod`
1×	`+-commutative` `sum-log` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `inv-pow` `associate-/l/`

Counts

4 → 316

Calls

4 calls:

199.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
292.0ms	(* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
111.0ms	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
398.0ms	(+ (* (* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
184.0ms	(* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
188.0ms	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
353.0ms	(+ (* (* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

simplify1.6s

Counts

328 → 328

Iterations

Iter	Nodes
done	2001
2	2001
1	1276
0	489

prune5.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

regimes313.0ms

Accuracy

1.9% (7.9b remaining)

Error of 12.4b against oracle of 4.5b and baseline of 12.5b

bsearch48.0ms

Steps

Iters	Range		Point
4	2.1870086748658e+79	4.3381537141120894e+79	4.246640781335346e+79

simplify8.0ms

Iterations

Iter	Nodes
done	39
1	39
0	31

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	6330×	body	80	valid
429.0ms	527×	body	1280	valid
421.0ms	599×	body	640	valid
322.0ms	8000×	pre	80	true
176.0ms	363×	body	320	valid
80.0ms	181×	body	160	valid