Details

sample86.0ms

Algorithm

intervals

Results

36.0ms	205×	body	80	valid
12.0ms	21×	body	1280	valid
10.0ms	256×	pre	80	true
7.0ms	16×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	6×	body	160	valid

simplify929.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (- beta alpha))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.3b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
21.0b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite868.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity` `times-frac`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `associate-/r/` `flip-+`
12×	`distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
8×	`frac-times`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`associate-l` `associate-l/` `associate-r/` `insert-posit16`
3×	`prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

26.0ms	(* (+ alpha beta) (- beta alpha))
190.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
584.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
64.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series835.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (+ alpha beta) (- beta alpha))
317.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
364.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
98.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify1.1s

Counts

160 → 160

Iterations

Iter	Nodes
done	2000
2	2000
1	789
0	267

prune889.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize53.0ms

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)))
3.7b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite650.0ms

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:

31.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
139.0ms	(/ (/ (- 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)))
94.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
257.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
291.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
432.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.6s

Counts

311 → 311

Iterations

Iter	Nodes
done	2005
2	2005
1	1128
0	389

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.1b	(* (+ alpha beta) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.4b	(log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
3.7b	(+ (* (+ alpha beta) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite824.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
181×	`*-un-lft-identity`
134×	`add-sqr-sqrt`
110×	`log-pow`
106×	`associate-r`
105×	`exp-prod`
91×	`add-cube-cbrt`
26×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`flip3-+` `flip-+`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/l*`
4×	`associate-l` `insert-posit16`
3×	`log-prod` `associate-/r*`
2×	`frac-times` `cbrt-undiv` `div-sub` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `log-div` `clear-num` `sum-log` `frac-2neg` `flip3--` `exp-diff` `rem-log-exp` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 219

Calls

4 calls:

59.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
565.0ms	(* (+ alpha beta) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
69.0ms	(log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
119.0ms	(+ (* (+ alpha beta) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series957.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
304.0ms	(* (+ alpha beta) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
132.0ms	(log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
423.0ms	(+ (* (+ alpha beta) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.4s

Counts

231 → 231

Iterations

Iter	Nodes
done	2003
2	2003
1	1039
0	373

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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)))
3.7b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
3.7b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite993.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
274×	`*-un-lft-identity`
195×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `flip-+`
11×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`log-prod` `associate-/r` `associate-l*` `log-pow` `insert-posit16`
3×	`exp-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `div-sub` `associate-*l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 275

Calls

4 calls:

200.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
354.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
349.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
83.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

251.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
373.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
392.0ms	(log (exp (+ (* (+ 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))) 1.0)

simplify1.5s

Counts

287 → 287

Iterations

Iter	Nodes
done	2007
2	2007
1	1132
0	398

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

regimes485.0ms

Accuracy

15.7% (5.3b remaining)

Error of 11.1b against oracle of 5.8b and baseline of 12.1b

bsearch2.0ms

Steps

Iters	Range		Point
0	1.3411925364794105e+213	1.351568782861715e+213	1.3451371616542299e+213

simplify20.0ms

Iterations

Iter	Nodes
done	46
1	46
0	35

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	6394×	body	80	valid
529.0ms	345×	body	320	valid
447.0ms	513×	body	1280	valid
430.0ms	8000×	pre	80	true
315.0ms	560×	body	640	valid
56.0ms	188×	body	160	valid