Details

sample61.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1807
2	295
1	60
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ beta (+ alpha i)) i (* beta alpha))
0.1b	(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
38.0b	(/ (/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
45.3b	(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
26×	`times-frac`
22×	`add-sqr-sqrt`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
7×	`div-inv`
6×	`associate-/l*` `difference-of-squares`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l/` `associate-r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow-prod-down` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-/r/` `flip-+`
1×	`flip3--` `associate-r` `*-commutative` `fma-udef` `flip--`

Counts

4 → 119

Calls

4 calls:

0.0ms	(fma (+ beta (+ alpha i)) i (* beta alpha))
81.0ms	(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
85.0ms	(/ (/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
94.0ms	(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

series1.1s

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma (+ beta (+ alpha i)) i (* beta alpha))
205.0ms	(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
481.0ms	(/ (/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
339.0ms	(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

simplify2.2s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	4921
1	687
0	221

prune882.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))
0.1b	(* (/ (/ (fma i (+ (+ alpha i) beta) (* beta alpha)) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))))
7.7b	(/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i)))
35.6b	(/ (fma i (+ (+ alpha i) beta) (* beta alpha)) (fma 2.0 i (+ alpha beta)))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
109×	`*-un-lft-identity`
84×	`add-sqr-sqrt`
74×	`add-cbrt-cube` `add-exp-log`
66×	`add-cube-cbrt`
64×	`associate-l`
30×	`cbrt-undiv` `div-exp`
27×	`associate-r`
22×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
12×	`associate-/r/`
9×	`div-inv`
8×	`pow1` `associate-/l*`
7×	`frac-times` `associate-*l/`
6×	`flip3--` `flip--`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `associate-/r` `associate-r/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `pow-prod-down` `*-commutative` `flip-+` `difference-of-squares` `associate-/l/`
1×	`sqrt-prod` `distribute-lft-out--`

Counts

4 → 219

Calls

4 calls:

45.0ms	(* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))
221.0ms	(* (/ (/ (fma i (+ (+ alpha i) beta) (* beta alpha)) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))))
95.0ms	(/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i)))
8.0ms	(/ (fma i (+ (+ alpha i) beta) (* beta alpha)) (fma 2.0 i (+ alpha beta)))

series4.0s

Counts

4 → 12

Calls

4 calls:

300.0ms	(* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))
3.1s	(* (/ (/ (fma i (+ (+ alpha i) beta) (* beta alpha)) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))))
445.0ms	(/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i)))
146.0ms	(/ (fma i (+ (+ alpha i) beta) (* beta alpha)) (fma 2.0 i (+ alpha beta)))

simplify497.0ms

Counts

231 → 231

Iterations

Iter	Nodes
done	5001
1	1174
0	372

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 0.5 i) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
0.1b	(* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))
0.1b	(* (/ (* 0.5 i) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))))
7.7b	(/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-cbrt-cube` `add-exp-log`
43×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
28×	`times-frac`
27×	`cbrt-undiv` `div-exp` `associate-r` `prod-exp` `cbrt-unprod`
20×	`add-cube-cbrt`
16×	`associate-l`
14×	`associate-/r/`
12×	`distribute-lft-out`
8×	`pow1`
7×	`frac-times` `associate-*l/`
6×	`flip3--` `flip--` `associate-/l*`
5×	`associate-/r*` `div-inv`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative` `difference-of-squares` `associate-/l/`
1×	`sqrt-prod` `distribute-lft-out--`

Counts

4 → 167

Calls

4 calls:

19.0ms	(/ (* 0.5 i) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
35.0ms	(* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))
153.0ms	(* (/ (* 0.5 i) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))))
74.0ms	(/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i)))

series2.6s

Counts

4 → 12

Calls

4 calls:

523.0ms	(/ (* 0.5 i) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
285.0ms	(* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))
1.4s	(* (/ (* 0.5 i) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))))
417.0ms	(/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i)))

simplify539.0ms

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
1	961
0	299

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i))
0.1b	(* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))
1.0b	(exp (log (/ (* 0.5 (* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))) (+ (sqrt 1.0) (fma 2.0 i (+ beta alpha))))))
3.0b	(log (/ (* 0.5 (* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))) (+ (sqrt 1.0) (fma 2.0 i (+ beta alpha)))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

2419×	`times-frac`
1930×	`*-un-lft-identity`
1404×	`add-sqr-sqrt`
846×	`add-cube-cbrt`
488×	`distribute-lft-out`
473×	`associate-r`
270×	`difference-of-squares`
135×	`sqrt-prod` `distribute-lft-out--`
104×	`div-inv`
68×	`add-exp-log`
60×	`associate-/r/`
36×	`associate-/l*`
34×	`add-cbrt-cube`
31×	`div-exp`
27×	`flip3--` `flip--`
20×	`log-prod`
16×	`cbrt-undiv` `prod-exp`
13×	`associate-/r*`
10×	`exp-sum`
8×	`pow1` `rem-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`log-div` `flip3-+` `log-pow` `flip-+`
1×	`clear-num` `frac-2neg` `exp-diff` `pow-prod-down` `associate-r/` `-commutative` `rem-exp-log` `associate-/l/`

Counts

4 → 1096

Calls

4 calls:

103.0ms	(/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i))
246.0ms	(* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))
774.0ms	(exp (log (/ (* 0.5 (* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))) (+ (sqrt 1.0) (fma 2.0 i (+ beta alpha))))))
251.0ms	(log (/ (* 0.5 (* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))) (+ (sqrt 1.0) (fma 2.0 i (+ beta alpha)))))

series6.7s

Counts

4 → 12

Calls

4 calls:

391.0ms	(/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i))
346.0ms	(* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))
1.3s	(exp (log (/ (* 0.5 (* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))) (+ (sqrt 1.0) (fma 2.0 i (+ beta alpha))))))
4.7s	(log (/ (* 0.5 (* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))) (+ (sqrt 1.0) (fma 2.0 i (+ beta alpha)))))

simplify2.6s

Counts

1108 → 1108

Iterations

Iter	Nodes
done	5002
1	3336
0	987

prune6.8s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 7.1b

regimes829.0ms

Accuracy

40.1% (4.7b remaining)

Error of 10.5b against oracle of 5.9b and baseline of 13.6b

bsearch54.0ms

Steps

Iters	Range		Point
5	1.3902498371092756e+121	3.7583810281082127e+121	3.6157084692163755e+121

simplify6.0ms

Iterations

Iter	Nodes
done	49
2	49
1	48
0	39

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
268.0ms	8000×	pre	80	true