Details

sample69.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (49.0ms)

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.4b	(/ (/ (* (* 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))
43.6b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite973.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 208

Calls

4 calls:

205.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
143.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
398.0ms	(/ (/ (* (* 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))
201.0ms	(/ (* (* 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:

108.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
170.0ms	(* (* 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))
288.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify893.0ms

Counts

220 → 220

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	366	12421
1	1232	11265
done	5000	9611

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 35.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ (+ i (+ alpha beta)) (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))) (/ i (fma 2.0 i (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta)))))
37.2b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
37.2b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
38.9b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log` `add-cbrt-cube`
33×	`prod-exp` `cbrt-unprod`
24×	`cbrt-undiv` `div-exp`
12×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`times-frac` `sqrt-prod`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative`

Counts

4 → 110

Calls

4 calls:

161.0ms	(* (* (/ (+ i (+ alpha beta)) (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))) (/ i (fma 2.0 i (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta)))))
2.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
7.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
20.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

series2.5s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (* (/ (+ i (+ alpha beta)) (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))) (/ i (fma 2.0 i (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta)))))
432.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
427.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
428.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

simplify2.8s

Counts

122 → 122

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	210	7761
1	592	7251
2	2555	4435
done	5000	4427

prune605.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 35.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (+ i (+ alpha beta)) (/ i (fma 2.0 i (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta)))))
37.2b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
37.2b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
38.9b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
19×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
11×	`pow1` `cbrt-undiv` `div-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`frac-times` `associate-*l/`
7×	`associate-r`
6×	`times-frac` `sqrt-prod`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative`

Counts

4 → 102

Calls

4 calls:

138.0ms	(* (* (+ i (+ alpha beta)) (/ i (fma 2.0 i (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta)))))
3.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
3.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
24.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

series3.8s

Counts

4 → 12

Calls

4 calls:

2.5s	(* (* (+ i (+ alpha beta)) (/ i (fma 2.0 i (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta)))))
448.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
387.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
490.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

simplify1.8s

Counts

114 → 114

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	209	5366
1	604	5084
2	2632	3993
done	5001	3982

prune641.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 35.3b

localize25.0ms

Local error

Found 4 expressions with local error:

37.2b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
37.2b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
38.9b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))
38.9b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `times-frac` `sqrt-prod` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

1.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
1.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
10.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))
9.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

series1.6s

Counts

4 → 12

Calls

4 calls:

447.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
327.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
424.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))
396.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma 2.0 i (+ alpha beta))))

simplify2.6s

Counts

88 → 88

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	111	2976
1	261	2810
2	834	2424
3	4017	2404
done	5000	2400

prune630.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 35.3b

regimes175.0ms

Accuracy

19% (2.9b remaining)

Error of 39.1b against oracle of 36.2b and baseline of 39.8b

bsearch18.0ms

Steps

Iters	Range		Point
2	9.31240604643187e+116	1.0720328448454475e+117	1.054433814820165e+117

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	103
1	34	103
done	34	103

end0.0ms

sample1.1s

Algorithm

intervals

Results

536.0ms	8000×	body	80	valid
173.0ms	8000×	pre	80	true