Details

sample80.0ms

Algorithm

intervals

Results

31.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1627
2	280
1	60
0	17

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.5b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha)))
0.1b	(* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i))
35.9b	(/ (/ (* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i)) (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha)))) (- (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha))) 1.0))
47.5b	(/ (* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i)) (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha))))

rewrite600.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

15.0ms	(* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha)))
164.0ms	(* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i))
214.0ms	(/ (/ (* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i)) (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha)))) (- (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha))) 1.0))
195.0ms	(/ (* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i)) (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha))))

series1.6s

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha)))
288.0ms	(* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i))
659.0ms	(/ (/ (* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i)) (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha)))) (- (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha))) 1.0))
518.0ms	(/ (* (fma beta alpha (* (+ (+ beta alpha) i) i)) (* (+ (+ beta alpha) i) i)) (* (fma 2.0 i (+ beta alpha)) (fma 2.0 i (+ beta alpha))))

simplify4.3s

Counts

150 → 150

Iterations

Iter	Nodes
done	5002
2	3356
1	714
0	245

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.7b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (* (+ (+ beta alpha) i) i) (fma 2.0 i (+ beta alpha))) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
0.3b	(/ (/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
34.5b	(/ (* (+ (+ beta alpha) i) i) (fma 2.0 i (+ beta alpha)))
34.8b	(/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
129×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
25×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/l*`
16×	`associate-/r*` `div-inv` `difference-of-squares`
14×	`distribute-lft-out`
11×	`cbrt-undiv` `div-exp`
8×	`sqrt-prod` `distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`flip3-+` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+`
1×	`flip3--` `flip--`

Counts

4 → 218

Calls

4 calls:

109.0ms	(/ (/ (* (+ (+ beta alpha) i) i) (fma 2.0 i (+ beta alpha))) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
43.0ms	(/ (/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
87.0ms	(/ (* (+ (+ beta alpha) i) i) (fma 2.0 i (+ beta alpha)))
11.0ms	(/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha)))

series1.5s

Counts

4 → 12

Calls

4 calls:

555.0ms	(/ (/ (* (+ (+ beta alpha) i) i) (fma 2.0 i (+ beta alpha))) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
582.0ms	(/ (/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
178.0ms	(/ (* (+ (+ beta alpha) i) i) (fma 2.0 i (+ beta alpha)))
235.0ms	(/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha)))

simplify4.1s

Counts

230 → 230

Iterations

Iter	Nodes
done	5000
2	2813
1	867
0	343

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.7b

localize96.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
0.3b	(/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i))
0.3b	(/ (/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
34.8b	(/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha)))

rewrite557.0ms

Algorithm

rewrite-expression-head

Rules

1415×	`times-frac`
1226×	`*-un-lft-identity`
815×	`add-sqr-sqrt`
531×	`add-cube-cbrt`
329×	`distribute-lft-out`
142×	`difference-of-squares`
91×	`associate-/l*`
71×	`sqrt-prod` `distribute-lft-out--`
57×	`div-inv`
26×	`associate-/r*`
25×	`add-exp-log` `add-cbrt-cube`
13×	`cbrt-undiv` `div-exp`
12×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`flip3-+` `flip-+`
1×	`flip3--` `flip--`

Counts

4 → 736

Calls

4 calls:

216.0ms	(/ (/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
147.0ms	(/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i))
45.0ms	(/ (/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
9.0ms	(/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha)))

series1.9s

Counts

4 → 12

Calls

4 calls:

646.0ms	(/ (/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
181.0ms	(/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i))
811.0ms	(/ (/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
265.0ms	(/ (fma beta alpha (* (+ (+ beta alpha) i) i)) (fma 2.0 i (+ beta alpha)))

simplify3.3s

Counts

748 → 748

Iterations

Iter	Nodes
done	5000
1	2012
0	754

prune5.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma 0.25 alpha (fma 0.5 i (* beta 0.25))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
0.3b	(/ (fma 2.0 i (+ beta alpha)) i)
0.3b	(/ (/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
0.3b	(/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i))

rewrite534.0ms

Algorithm

rewrite-expression-head

Rules

1330×	`times-frac`
1166×	`*-un-lft-identity`
775×	`add-sqr-sqrt`
491×	`add-cube-cbrt`
319×	`distribute-lft-out`
142×	`difference-of-squares`
81×	`associate-/l*`
71×	`sqrt-prod` `distribute-lft-out--`
52×	`div-inv`
26×	`associate-/r*`
22×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`flip3-+` `flip-+`
1×	`flip3--` `flip--`

Counts

4 → 683

Calls

4 calls:

27.0ms	(/ (fma 0.25 alpha (fma 0.5 i (* beta 0.25))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
10.0ms	(/ (fma 2.0 i (+ beta alpha)) i)
204.0ms	(/ (/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
152.0ms	(/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i))

series1.2s

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (fma 0.25 alpha (fma 0.5 i (* beta 0.25))) (+ (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
66.0ms	(/ (fma 2.0 i (+ beta alpha)) i)
601.0ms	(/ (/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0)))
203.0ms	(/ (+ (+ beta alpha) i) (/ (fma 2.0 i (+ beta alpha)) i))

simplify3.0s

Counts

695 → 695

Iterations

Iter	Nodes
done	5000
1	1760
0	672

prune5.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

regimes584.0ms

Accuracy

41% (9.5b remaining)

Error of 11.6b against oracle of 2.1b and baseline of 18.3b

bsearch125.0ms

Steps

Iters	Range		Point
6	5.49638027382935e+110	3.514303845479213e+111	3.3658994132753784e+111

simplify19.0ms

Iterations

Iter	Nodes
done	42
1	42
0	34

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
971.0ms	8000×	pre	80	true