Details

sample45.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	295	48
3	1651	48
done	5002	48

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.5b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.3b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
42×	`add-sqr-sqrt`
32×	`frac-times`
31×	`*-un-lft-identity`
30×	`associate-*r/`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
11×	`pow1`
9×	`associate-/l/`
8×	`associate-r`
7×	`div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 197

Calls

4 calls:

107.0ms	(* i (+ (+ alpha beta) i))
181.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
368.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
674.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* i (+ (+ alpha beta) i))
145.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
315.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify743.0ms

Counts

209 → 209

Iterations

Useful iterations: done (732.0ms)

Iter	Nodes	Cost
0	353	11780
1	1190	10755
done	5000	9194

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 37.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
4.0b	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
37.5b	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
41.7b	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
61×	`add-exp-log` `add-cbrt-cube`
57×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
29×	`cbrt-undiv` `div-exp`
15×	`div-inv`
14×	`associate-/r` `associate-/l`
13×	`difference-of-squares`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `associate-/l/`
2×	`associate-*r/` `fma-udef`
1×	`pow2` `distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 187

Calls

4 calls:

14.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
63.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
206.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
22.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.9s

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
290.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.3s	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
204.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.5s

Counts

199 → 199

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	330	10445
1	909	9614
2	3975	8391
done	5001	7837

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
3.9b	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
37.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
37.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

2093×	`times-frac`
1742×	`*-un-lft-identity`
1206×	`add-sqr-sqrt`
740×	`add-cube-cbrt`
462×	`distribute-lft-out`
437×	`sqrt-prod`
232×	`difference-of-squares`
118×	`associate-/l*`
116×	`distribute-lft-out--`
44×	`div-inv`
22×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
10×	`cbrt-undiv` `div-exp`
7×	`associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `flip-+`
1×	`flip3--` `associate-*r/` `flip--` `associate-/l/`

Counts

4 → 892

Calls

4 calls:

190.0ms	(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
30.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.4s

Counts

4 → 12

Calls

4 calls:

434.0ms	(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
774.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
89.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
87.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.4s

Counts

904 → 904

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	820	56632
1	2132	53860
done	5000	53067

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
3.8b	(/ (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) i)
37.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
37.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

2093×	`times-frac`
1742×	`*-un-lft-identity`
1206×	`add-sqr-sqrt`
740×	`add-cube-cbrt`
462×	`distribute-lft-out`
437×	`sqrt-prod`
232×	`difference-of-squares`
116×	`associate-/l*` `distribute-lft-out--`
44×	`div-inv`
22×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
9×	`associate-/r*` `associate-/r/`
6×	`pow1` `associate-/l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `flip-+`
1×	`flip3--` `associate-*r/` `flip--`

Counts

4 → 892

Calls

4 calls:

160.0ms	(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
43.0ms	(/ (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) i)
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts

4 → 12

Calls

4 calls:

443.0ms	(/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
573.0ms	(/ (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) i)
98.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
85.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.7s

Counts

904 → 904

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	832	56641
1	2180	53854
done	5000	53061

prune3.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 36.4b

regimes189.0ms

Accuracy

31.3% (2.4b remaining)

Error of 36.7b against oracle of 34.3b and baseline of 37.8b

bsearch96.0ms

Steps

Iters	Range		Point
9	1.2915363516181262e+203	4.3902837048076336e+209	1.3081371896109472e+203

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	72
1	32	72
done	32	72

end0.0ms

sample2.0s

Algorithm

intervals

Results

876.0ms	8000×	body	80	valid
754.0ms	8000×	pre	80	true