Details

sample60.0ms

Algorithm

intervals

Results

12.0ms	37×	body	1280	valid
11.0ms	174×	body	80	valid
7.0ms	256×	pre	80	true
5.0ms	21×	body	640	valid
3.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify664.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	52	13
4	73	13
5	118	13
6	161	13
7	199	13
8	230	13
9	268	13
10	296	13
11	307	13
12	319	13
13	323	13
done	323	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

66.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
306.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series145.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
90.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.3s

Counts

106 → 106

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	128	1178
1	335	1110
2	950	1056
3	3094	1048
done	5001	1043

prune388.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
116×	`times-frac`
93×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
12×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 229

Calls

4 calls:

1.9s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
78.0ms	(/ beta (+ (+ alpha beta) 2.0))
74.0ms	(/ alpha (+ (+ alpha beta) 2.0))
384.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series375.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
67.0ms	(/ beta (+ (+ alpha beta) 2.0))
82.0ms	(/ alpha (+ (+ alpha beta) 2.0))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

241 → 241

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	308	5116
1	713	4369
2	1884	3978
done	5000	3802

prune683.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))
1.8b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

1026×	`*-un-lft-identity`
576×	`prod-diff`
531×	`times-frac`
522×	`add-sqr-sqrt`
464×	`add-cube-cbrt`
456×	`unpow-prod-down` `cube-prod`
324×	`distribute-lft-out`
99×	`associate-*r/`
89×	`flip3-+` `flip-+`
72×	`sqr-pow`
66×	`associate-/r/` `associate-/l/`
64×	`frac-sub`
62×	`cube-mult` `unpow3`
49×	`frac-times`
48×	`fma-neg` `frac-add`
39×	`swap-sqr`
33×	`associate-*l/` `div-inv`
28×	`add-exp-log` `add-cbrt-cube`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
21×	`associate-r` `associate-l`
12×	`pow1`
8×	`cbrt-undiv` `div-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 937

Calls

4 calls:

253.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
56.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
395.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))
758.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series934.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
77.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
628.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))
139.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify1.4s

Counts

949 → 949

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	698	43563
1	2235	30649
done	5001	26874

prune2.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))
0.6b	(exp (log (/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))))
1.8b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
11.3b	(log (/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta)))))

rewrite897.0ms

Algorithm

rewrite-expression-head

Rules

802×	`*-un-lft-identity`
576×	`prod-diff`
448×	`add-sqr-sqrt`
435×	`unpow-prod-down` `cube-prod`
407×	`times-frac`
402×	`add-cube-cbrt`
234×	`distribute-lft-out`
71×	`sqr-pow`
61×	`cube-mult` `unpow3`
58×	`associate-/r/`
48×	`fma-neg`
29×	`flip3-+` `flip-+` `div-inv`
24×	`difference-of-squares`
23×	`add-exp-log`
18×	`log-prod`
13×	`add-cbrt-cube`
9×	`exp-sum`
6×	`pow1` `associate-*r/` `div-exp` `prod-exp` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `exp-prod` `rem-log-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `cbrt-unprod` `associate-/l*`
2×	`log-div` `log-pow`
1×	`difference-cubes` `sub-neg` `flip3--` `frac-2neg` `exp-diff` `diff-log` `clear-num` `associate-/r*` `flip--` `rem-exp-log`

Counts

4 → 743

Calls

4 calls:

33.0ms	(/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))
134.0ms	(exp (log (/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))))
604.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
44.0ms	(log (/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

572.0ms	(/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))
554.0ms	(exp (log (/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta))))))
119.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
390.0ms	(log (/ (fma (fma 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (pow (/ alpha (+ 2.0 (+ alpha beta))) 2)) beta (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (* 2.0 (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (+ 2.0 (+ alpha beta)))))

simplify2.8s

Counts

755 → 755

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	554	37217
1	1371	25999
2	4297	20286
done	5000	20285

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

regimes196.0ms

Accuracy

65.3% (5.2b remaining)

Error of 5.9b against oracle of 0.8b and baseline of 15.6b

bsearch62.0ms

Steps

Iters	Range		Point
5	879064267.884121	3030780229.4257846	1845090834.437638

simplify22.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	119
1	53	119
2	65	119
3	69	119
done	69	119

end0.0ms

sample1.9s

Algorithm

intervals

Results

881.0ms	5878×	body	80	valid
299.0ms	844×	body	1280	valid
169.0ms	697×	body	640	valid
156.0ms	8000×	pre	80	true
55.0ms	381×	body	320	valid
19.0ms	200×	body	160	valid