Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
5.0ms	27×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	16×	body	640	valid
1.0ms	6×	body	160	valid
0.0ms	5×	body	320	valid

simplify628.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.7b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite386.0ms

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:

89.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
285.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series161.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
110.0ms	(+ (/ (- 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

prune413.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite509.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 179

Calls

3 calls:

73.0ms	(/ alpha (+ (+ alpha beta) 2.0))
67.0ms	(/ beta (+ (+ alpha beta) 2.0))
347.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series244.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ alpha (+ (+ alpha beta) 2.0))
76.0ms	(/ beta (+ (+ alpha beta) 2.0))
112.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.3s

Counts

188 → 188

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	221	3563
1	492	2856
2	1159	2541
3	3589	2285
done	5000	2285

prune585.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
0.0b	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite858.0ms

Algorithm

rewrite-expression-head

Rules

167×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
80×	`times-frac`
77×	`add-cube-cbrt`
63×	`prod-diff`
48×	`distribute-lft-out`
21×	`fma-neg`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod`
10×	`associate-/r/` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `associate-/r*` `flip-+` `div-inv` `distribute-lft-out--`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `flip--` `associate-/l*`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 204

Calls

4 calls:

50.0ms	(/ beta (+ (+ alpha beta) 2.0))
195.0ms	(cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
252.0ms	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
339.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series660.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ beta (+ (+ alpha beta) 2.0))
164.0ms	(cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
305.0ms	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
123.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

216 → 216

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	288	4532
1	666	3628
2	1720	3223
done	5001	3049

prune530.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
12.9b	(fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
15×	`times-frac`
12×	`add-sqr-sqrt` `add-cube-cbrt` `distribute-lft-out`
6×	`add-exp-log`
5×	`associate-/r*`
4×	`add-cbrt-cube`
3×	`pow1` `associate-/l*`
2×	`expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 53

Calls

2 calls:

82.0ms	(/ 1 (+ (+ alpha beta) 2.0))
1.0ms	(fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0)

series160.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ 1 (+ (+ alpha beta) 2.0))
89.0ms	(fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0)

simplify2.4s

Counts

59 → 59

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	94	705
1	203	621
2	499	555
3	1609	554
done	5000	551

prune155.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes134.0ms

Accuracy

77.4% (2.9b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 16.0b

bsearch66.0ms

Steps

Iters	Range		Point
9	5.185608013011847	8177076.526676658	8092481.162986399

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	43
1	31	43
done	31	43

end0.0ms

sample1.6s

Algorithm

intervals

Results

427.0ms	828×	body	1280	valid
385.0ms	5798×	body	80	valid
166.0ms	8000×	pre	80	true
152.0ms	703×	body	640	valid
111.0ms	441×	body	320	valid
25.0ms	230×	body	160	valid