Details

sample89.0ms

Algorithm

intervals

Results

26.0ms	199×	body	80	valid
14.0ms	19×	body	1280	valid
11.0ms	256×	pre	80	true
11.0ms	21×	body	640	valid
3.0ms	8×	body	320	valid
3.0ms	9×	body	160	valid

simplify766.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2315
3	458
2	99
1	32
0	16

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.7b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b

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

2.6b

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

21.7b

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-/l/`
7×	`fma-def`
6×	`times-frac`
5×	`add-log-exp`
4×	`frac-times` `flip3-+` `flip-+`
3×	`expm1-log1p-u` `associate-/r` `flip3--` `swap-sqr` `associate-r` `associate-l*` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow2` `distribute-rgt-in` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `pow-plus` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

11.0ms

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

35.0ms

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

28.0ms

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

series768.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms

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

255.0ms

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

415.0ms

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

simplify4.5s

Counts

93 → 93

Iterations

Iter	Nodes
3	8196
2	1683
1	473
0	165

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.0b

localize102.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
0.1b	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
2.6b	(fma (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* 1.0 (* 1.0 1.0)))
2.9b	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
90×	`add-sqr-sqrt` `times-frac`
62×	`associate-r`
46×	`add-cube-cbrt` `distribute-lft-out`
44×	`associate-l`
28×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `prod-diff`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--`

Counts

4 → 192

Calls

4 calls:

127.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
145.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
0.0ms	(fma (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* 1.0 (* 1.0 1.0)))
9.0ms	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

series4.0s

Counts

4 → 12

Calls

4 calls:

641.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
414.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
2.7s	(fma (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* 1.0 (* 1.0 1.0)))
264.0ms	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

simplify985.0ms

Counts

204 → 204

Iterations

Iter	Nodes
2	2227
1	650
0	221

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
0.1b	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
2.6b	(+ (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) (* 1.0 (* 1.0 1.0)))
2.9b	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
90×	`add-sqr-sqrt` `times-frac`
62×	`associate-r`
46×	`add-cube-cbrt` `distribute-lft-out`
44×	`associate-l`
28×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `prod-diff`
2×	`frac-times` `cube-unmult` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`
1×	`+-commutative` `sum-log` `sub-neg` `fma-def` `flip3--` `diff-log` `sum-cubes` `flip--`

Counts

4 → 197

Calls

4 calls:

103.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
101.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
785.0ms	(+ (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) (* 1.0 (* 1.0 1.0)))
9.0ms	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

series6.7s

Counts

4 → 12

Calls

4 calls:

348.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
319.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
5.7s	(+ (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) (* 1.0 (* 1.0 1.0)))
269.0ms	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

simplify1.5s

Counts

209 → 209

Iterations

Iter	Nodes
2	2845
1	745
0	238

prune3.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize107.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
2.5b	(log1p (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))
2.6b	(+ (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) (* 1.0 (* 1.0 1.0)))
2.9b	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

rewrite793.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
45×	`times-frac`
31×	`associate-r`
26×	`add-cube-cbrt`
23×	`distribute-lft-out`
22×	`associate-l`
16×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`pow1`
5×	`expm1-log1p-u` `distribute-lft-out--` `difference-of-squares`
4×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`flip3-+` `fma-neg` `prod-diff` `flip-+`
2×	`cube-unmult` `div-inv`
1×	`frac-times` `+-commutative` `log1p-udef` `sum-log` `sub-neg` `fma-def` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `log1p-expm1` `associate-r/` `sum-cubes` `*-commutative` `flip--`

Counts

4 → 129

Calls

4 calls:

88.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
0.0ms	(log1p (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))
697.0ms	(+ (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) (* 1.0 (* 1.0 1.0)))
5.0ms	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

series7.1s

Counts

4 → 12

Calls

4 calls:

295.0ms	(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
778.0ms	(log1p (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))
5.8s	(+ (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) (* 1.0 (* 1.0 1.0)))
287.0ms	(- 1.0 (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))

simplify1.6s

Counts

141 → 141

Iterations

Iter	Nodes
2	3064
1	840
0	267

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

regimes303.0ms

Accuracy

13.3% (5.5b remaining)

Error of 11.5b against oracle of 6.0b and baseline of 12.4b

bsearch168.0ms

Steps

Iters	Range		Point
7	2.1027794302435606e+105	3.5400380850047944e+106	3.158427829609547e+106

simplify20.0ms

Iterations

Iter	Nodes
2	63
1	63
0	51

end0.0ms

sample3.2s

Algorithm

intervals

Results

966.0ms	8000×	pre	80	true
952.0ms	6351×	body	80	valid
448.0ms	568×	body	640	valid
412.0ms	520×	body	1280	valid
152.0ms	347×	body	320	valid
58.0ms	214×	body	160	valid