Details

sample67.0ms

Algorithm

intervals

Results

26.0ms	206×	body	80	valid
9.0ms	256×	pre	80	true
8.0ms	21×	body	640	valid
5.0ms	11×	body	1280	valid
5.0ms	17×	body	320	valid
0.0ms	1×	body	160	valid

simplify933.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.7b

localize53.0ms

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))

0.7b

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

21.4b

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

0.0ms

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

27.0ms

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

23.0ms

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

series883.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms

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

301.0ms

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

434.0ms

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

simplify1.0s

Counts

74 → 74

Iterations

Iter	Nodes
done	2000
3	2000
2	1464
1	411
0	137

prune856.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
2.7b	(log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
12.1b	(fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)
17.1b	(/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

3.0ms	(exp (log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
1.0ms	(log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
0.0ms	(fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)
27.0ms	(/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

382.0ms	(exp (log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
381.0ms	(log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
373.0ms	(fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)
245.0ms	(/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0)))

simplify1.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	2018
3	2018
2	1480
1	400
0	164

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0))
0.2b	(exp (log (fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0)))
2.7b	(log (fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0))
12.1b	(fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

26.0ms	(/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0))
3.0ms	(exp (log (fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0)))
2.0ms	(log (fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0))
1.0ms	(fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0))
377.0ms	(exp (log (fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0)))
403.0ms	(log (fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0))
390.0ms	(fma (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha) 1.0)

simplify1.3s

Counts

160 → 160

Iterations

Iter	Nodes
done	2028
3	2028
2	1618
1	591
0	256

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0)))
1.2b	(* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha))
2.7b	(log (+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0))
2.9b	(+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0)

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
115×	`times-frac`
92×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
70×	`associate-l`
36×	`prod-diff`
28×	`distribute-lft-out`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
14×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`associate-r` `div-inv`
4×	`expm1-log1p-u` `log-div` `exp-prod` `sub-neg` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `exp-sum` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `flip3--` `exp-diff` `associate-*r/` `associate-/r/` `log-pow` `flip--`
1×	`+-commutative` `sum-log` `fma-def` `rem-log-exp` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

4 → 197

Calls

4 calls:

37.0ms	(exp (log (+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0)))
88.0ms	(* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha))
37.0ms	(log (+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0))
34.0ms	(+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0)

series1.6s

Counts

4 → 12

Calls

4 calls:

405.0ms	(exp (log (+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0)))
327.0ms	(* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha))
423.0ms	(log (+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0))
408.0ms	(+ (* (/ (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (+ (fma i 2 (+ alpha beta)) 2.0)) (- beta alpha)) 1.0)

simplify1.1s

Counts

209 → 209

Iterations

Iter	Nodes
done	2001
2	2001
1	938
0	350

prune3.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

regimes357.0ms

Accuracy

2.9% (8.0b remaining)

Error of 12.4b against oracle of 4.5b and baseline of 12.7b

bsearch55.0ms

Steps

Iters	Range		Point
4	2.1870086748658e+79	4.3381537141120894e+79	3.880589050228373e+79

simplify31.0ms

Iterations

Iter	Nodes
done	42
1	42
0	34

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	6330×	body	80	valid
854.0ms	8000×	pre	80	true
444.0ms	599×	body	640	valid
409.0ms	527×	body	1280	valid
201.0ms	363×	body	320	valid
52.0ms	181×	body	160	valid