Details

sample81.0ms

Algorithm

intervals

Results

32.0ms	197×	body	80	valid
12.0ms	20×	body	1280	valid
9.0ms	256×	pre	80	true
9.0ms	19×	body	640	valid
6.0ms	16×	body	320	valid
1.0ms	4×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2067
4	2067
3	458
2	99
1	32
0	16

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ beta alpha) (- beta alpha))
0.0b	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
1.8b	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
23.6b	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `add-exp-log`
8×	`frac-times` `associate-/l/`
7×	`fma-def` `flip3-+` `flip-+`
6×	`pow1` `times-frac` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`cbrt-undiv` `sub-neg` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `-commutative` `fma-udef` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

34.0ms	(* (+ beta alpha) (- beta alpha))
0.0ms	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
21.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
20.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

series980.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (+ beta alpha) (- beta alpha))
180.0ms	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
320.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
417.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

simplify874.0ms

Counts

131 → 131

Iterations

Iter	Nodes
done	2001
2	2001
1	682
0	225

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.1b

localize61.0ms

Local error

Found 3 expressions with local error:

0.0b

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

14.2b

(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

18.5b

(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
13×	`add-cube-cbrt`
5×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

3 → 63

Calls

3 calls:

0.0ms

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

0.0ms

(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

20.0ms

(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

series726.0ms

Counts

3 → 9

Calls

3 calls:

157.0ms

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

287.0ms

(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

281.0ms

(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

simplify889.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	2000
3	2000
2	718
1	286
0	131

prune783.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)))
4.9b	(log (fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0))
14.2b	(fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)
18.5b	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`add-cbrt-cube` `add-cube-cbrt`
6×	`pow1` `log-prod`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `exp-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`cbrt-undiv` `div-exp` `associate-*r/` `associate-/r/` `log-pow` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `flip3--` `div-sub` `rem-log-exp` `prod-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `flip--` `rem-exp-log`

Counts

4 → 77

Calls

4 calls:

3.0ms	(exp (log (fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)))
1.0ms	(log (fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0))
0.0ms	(fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)
17.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

392.0ms	(exp (log (fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)))
382.0ms	(log (fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0))
316.0ms	(fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)
211.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

simplify1.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	2008
3	2008
2	1541
1	415
0	173

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma 2 i (+ alpha beta)))
0.2b	(exp (log (fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0)))
4.9b	(log (fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0))
14.2b	(fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0)

rewrite23.0ms

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` `insert-posit16` `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 → 85

Calls

4 calls:

18.0ms	(/ (- beta alpha) (fma 2 i (+ alpha beta)))
3.0ms	(exp (log (fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0)))
1.0ms	(log (fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0))
0.0ms	(fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- beta alpha) (fma 2 i (+ alpha beta)))
387.0ms	(exp (log (fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0)))
352.0ms	(log (fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0))
348.0ms	(fma (+ alpha beta) (/ (/ (- beta alpha) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) 2.0)) 1.0)

simplify892.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	2000
3	2000
2	895
1	351
0	166

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

regimes287.0ms

Accuracy

14.9% (7.3b remaining)

Error of 11.6b against oracle of 4.3b and baseline of 12.9b

bsearch76.0ms

Steps

Iters	Range		Point
6	2.310233354129206e+149	1.637278862402389e+150	1.0312336573895782e+150

simplify9.0ms

Iterations

Iter	Nodes
done	36
1	36
0	32

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	6303×	body	80	valid
661.0ms	636×	body	640	valid
472.0ms	494×	body	1280	valid
391.0ms	8000×	pre	80	true
152.0ms	373×	body	320	valid
52.0ms	194×	body	160	valid