Details

sample92.0ms

Algorithm

intervals

Results

21.0ms	16×	body	1280	valid
21.0ms	201×	body	80	valid
8.0ms	256×	pre	80	true
7.0ms	17×	body	640	valid
4.0ms	12×	body	320	valid
2.0ms	10×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2747
3	478
2	106
1	31
0	15

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

0.1b

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

12.7b

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
156×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
24×	`associate-/l*`
20×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`flip3-+` `flip3--` `flip-+` `fma-udef` `flip--`

Counts

3 → 169

Calls

3 calls:

29.0ms

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

56.0ms

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

1.0ms

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

series695.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

272.0ms

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

324.0ms

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

simplify1.5s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	2673
1	620
0	250

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
0.0b	(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
0.1b	(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
2.1b	(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
66×	`times-frac`
42×	`add-cube-cbrt`
22×	`associate-l`
20×	`add-cbrt-cube` `add-exp-log`
19×	`associate-r`
18×	`distribute-lft-out`
9×	`associate-/l*`
7×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `unswap-sqr` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `+-commutative` `sum-log` `fma-def` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 163

Calls

4 calls:

35.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
14.0ms	(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
87.0ms	(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
20.0ms	(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

series871.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
120.0ms	(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
363.0ms	(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
284.0ms	(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

simplify1.8s

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
2	4161
1	716
0	242

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
0.0b	(exp (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0))
2.1b	(log (exp (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)))
2.1b	(fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/r*` `fma-udef`
2×	`exp-sum` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `rem-log-exp` `div-inv` `flip--` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

15.0ms	(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
3.0ms	(exp (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0))
5.0ms	(log (exp (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)))
1.0ms	(fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
301.0ms	(exp (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0))
412.0ms	(log (exp (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)))
404.0ms	(fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)

simplify585.0ms

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1060
1	320
0	153

prune951.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
0.1b	(exp (log (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)))
2.1b	(fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)
2.4b	(log (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
7×	`add-exp-log`
6×	`pow1` `log-prod` `add-cbrt-cube`
5×	`associate-/l*`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r*` `exp-sum`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `rem-log-exp` `fma-udef` `div-inv` `flip--` `rem-exp-log`

Counts

4 → 81

Calls

4 calls:

24.0ms	(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
3.0ms	(exp (log (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)))
0.0ms	(fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)
1.0ms	(log (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
414.0ms	(exp (log (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)))
391.0ms	(fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0)
321.0ms	(log (fma (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 1.0))

simplify712.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1158
1	347
0	162

prune698.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.2b

regimes577.0ms

Accuracy

9.4% (7.1b remaining)

Error of 11.1b against oracle of 4.0b and baseline of 11.9b

bsearch312.0ms

Steps

Iters	Range		Point
8	7.771447136109609e+287	6.458252668035268e+291	8.077229676032387e+288
5	5.835558310822123e+276	1.6977225856336582e+277	1.6755828657974486e+277
7	4.644949955970094e+210	7.857719149395794e+212	1.244272110236543e+212

simplify5.0ms

Iterations

Iter	Nodes
done	53
1	53
0	46

end0.0ms

sample2.2s

Algorithm

intervals

Results

761.0ms	8000×	pre	80	true
566.0ms	6418×	body	80	valid
233.0ms	495×	body	1280	valid
197.0ms	572×	body	640	valid
69.0ms	321×	body	320	valid
28.0ms	194×	body	160	valid