Details

sample94.0ms

Algorithm

intervals

Results

53.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	2000
3	1615
2	280
1	60
0	17

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
0.1b	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
34.9b	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
46.2b	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-cbrt-cube` `add-exp-log`
22×	`times-frac`
21×	`add-sqr-sqrt`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`pow1`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`associate-/l*`
6×	`associate-l` `associate-/r/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `difference-of-squares`
3×	`flip3--` `swap-sqr` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `*-commutative` `flip-+` `fma-udef`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 136

Calls

4 calls:

12.0ms	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
63.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
87.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
98.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))
223.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
426.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
890.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

simplify1.1s

Counts

148 → 148

Iterations

Iter	Nodes
done	2003
2	2003
1	727
0	253

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
0.1b	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
34.5b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
34.8b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
188×	`*-un-lft-identity`
169×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
70×	`add-cbrt-cube` `add-exp-log`
58×	`associate-l`
40×	`associate-r`
33×	`cbrt-undiv` `div-exp`
25×	`distribute-lft-out`
24×	`associate-/r/`
22×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
15×	`div-inv`
13×	`associate-/r*`
10×	`difference-of-squares`
9×	`flip3-+` `flip-+`
6×	`pow1` `unswap-sqr`
5×	`sqrt-prod` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*l/` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 306

Calls

4 calls:

21.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
111.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
77.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
19.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series1.9s

Counts

4 → 12

Calls

4 calls:

432.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
784.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
262.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
445.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.5s

Counts

318 → 318

Iterations

Iter	Nodes
done	2001
2	2001
1	1513
0	462

prune4.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 34.4b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (fma 2 i (+ alpha beta)) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
0.1b	(* (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
34.5b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
34.8b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

1087×	`times-frac`
605×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
455×	`add-cube-cbrt`
220×	`add-exp-log`
182×	`associate-l`
128×	`div-exp`
100×	`add-cbrt-cube`
69×	`associate-/r*`
67×	`distribute-lft-out`
61×	`associate-/r/`
53×	`cbrt-undiv`
51×	`prod-exp`
40×	`associate-r`
36×	`div-inv`
23×	`flip3-+` `flip-+`
21×	`cbrt-unprod`
15×	`rec-exp` `1-exp`
14×	`unswap-sqr`
10×	`difference-of-squares`
7×	`pow1` `associate-/l*`
5×	`sqrt-prod` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*l/`
2×	`associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-r/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 644

Calls

4 calls:

15.0ms	(/ 1 (/ (fma 2 i (+ alpha beta)) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
115.0ms	(* (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
46.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
16.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series4.3s

Counts

4 → 12

Calls

4 calls:

374.0ms	(/ 1 (/ (fma 2 i (+ alpha beta)) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
3.3s	(* (/ 1 (/ (fma 2 i (+ alpha beta)) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))) (/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))))
242.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
409.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.8s

Counts

656 → 656

Iterations

Iter	Nodes
done	2001
1	2001
0	886

prune11.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 34.4b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (sqrt (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) 1)) (/ (sqrt (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (fma 2 i (+ alpha beta))))
34.5b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
34.5b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
34.8b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
87×	`times-frac`
81×	`add-cbrt-cube`
70×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
49×	`associate-r`
45×	`div-exp`
43×	`sqrt-prod`
42×	`add-cube-cbrt`
40×	`prod-exp`
30×	`cbrt-undiv`
28×	`cbrt-unprod`
16×	`associate-/r*`
14×	`difference-of-squares`
12×	`associate-/r/`
9×	`pow1` `associate-*l/`
7×	`div-inv` `distribute-lft-out--`
6×	`1-exp`
5×	`frac-times` `flip3--` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg` `flip3-+` `pow-prod-down` `associate-*r/` `flip-+`
1×	`associate-l` `*-commutative`

Counts

4 → 208

Calls

4 calls:

322.0ms	(* (* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (sqrt (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) 1)) (/ (sqrt (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (fma 2 i (+ alpha beta))))
71.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
52.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
9.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series1.9s

Counts

4 → 12

Calls

4 calls:

868.0ms	(* (* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta))) (/ (sqrt (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) 1)) (/ (sqrt (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (fma 2 i (+ alpha beta))))
286.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
252.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
509.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.4s

Counts

220 → 220

Iterations

Iter	Nodes
done	2001
2	2001
1	1109
0	367

prune4.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 34.4b

regimes293.0ms

Accuracy

0% (2.5b remaining)

Error of 36.3b against oracle of 33.9b and baseline of 36.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
444.0ms	8000×	pre	80	true