Details

sample67.0ms

Algorithm

intervals

Results

19.0ms	58×	body	1280	valid
16.0ms	59×	body	640	valid
5.0ms	95×	body	80	valid
4.0ms	29×	body	320	valid
4.0ms	90×	body	80	overflowed
2.0ms	16×	body	160	valid

simplify870.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	172	12
6	484	12
7	1568	12
done	5001	12

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp x) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
10.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series36.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
3.0ms	(- (exp (* 2.0 x)) 1.0)
11.0ms	(- (exp x) 1.0)

simplify681.0ms

Counts

135 → 135

Iterations

Useful iterations: done (670.0ms)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	963	2167
3	2538	2156
done	5000	2154

prune259.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 0.2b

Counts

136 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (/ x (sqrt 2.0))) (sqrt 2.0))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
4×	`prod-exp`
3×	`cbrt-undiv` `div-inv`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 217

Calls

4 calls:

7.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (sqrt 2.0))
22.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
7.0ms	(/ (pow x 2) (sqrt 2.0))
5.0ms	(/ x (sqrt 2.0))

series31.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (sqrt 2.0))
7.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
7.0ms	(/ (pow x 2) (sqrt 2.0))
6.0ms	(/ x (sqrt 2.0))

simplify537.0ms

Counts

229 → 229

Iterations

Useful iterations: done (530.0ms)

Iter	Nodes	Cost
0	269	3092
1	626	2896
2	2362	2591
done	5000	2577

prune504.0ms

Filtered

141 candidates to 229 candidates (-62.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	229	2	231

Merged error: 0.2b

Counts

231 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))
3.1b	(exp (log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
27.8b	(log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`sqrt-prod`
22×	`add-exp-log`
21×	`unpow-prod-down`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`pow1` `log-div`
8×	`add-cbrt-cube`
7×	`div-exp` `unpow2` `sqr-pow`
5×	`exp-prod` `exp-diff` `rem-log-exp`
4×	`frac-times` `flip3--` `associate-*r/` `prod-exp` `log-pow` `flip--` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `log-prod` `frac-2neg` `pow-prod-down` `associate-*l/` `pow-exp` `clear-num` `div-inv`
1×	`exp-sum` `rem-exp-log`

Counts

4 → 154

Calls

4 calls:

7.0ms	(/ (pow x 2) (sqrt 2.0))
5.0ms	(/ x (sqrt 2.0))
16.0ms	(exp (log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
14.0ms	(log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (pow x 2) (sqrt 2.0))
6.0ms	(/ x (sqrt 2.0))
7.0ms	(exp (log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
21.0ms	(log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))

simplify980.0ms

Counts

166 → 166

Iterations

Useful iterations: 3 (384.0ms)

Iter	Nodes	Cost
0	231	2119
1	422	1909
2	1242	1706
3	4902	1701
done	5000	1701

prune373.0ms

Filtered

98 candidates to 166 candidates (-69.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	165	3	168

Merged error: 0.2b

Counts

168 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

253×	`times-frac`
208×	`*-un-lft-identity`
178×	`add-sqr-sqrt`
135×	`sqrt-prod`
92×	`add-cube-cbrt`
79×	`difference-of-squares`
31×	`distribute-lft-out`
27×	`distribute-lft-out--`
26×	`exp-sum`
13×	`associate-/r/`
8×	`add-log-exp`
7×	`div-inv`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
5×	`pow1` `associate-/l*`
4×	`associate-/r*`
3×	`rem-sqrt-square` `flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 222

Calls

4 calls:

13.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
26.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
4.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series38.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
24.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
3.0ms	(- (exp (* 2.0 x)) 1.0)
3.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify793.0ms

Counts

234 → 234

Iterations

Useful iterations: 2 (310.0ms)

Iter	Nodes	Cost
0	510	7530
1	1088	7251
2	3469	6811
done	5000	6811

prune532.0ms

Filtered

158 candidates to 234 candidates (-48.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	233	4	237

Merged error: 0.2b

Counts

237 → 4

regimes48.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.0b

bsearch20.0ms

Steps

Iters	Range		Point
9	-0.0001616040529746431	-1.1951251334293225e-11	-1.2211091000924002e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	52
1	43	52
done	43	52

end0.0ms

sample1.7s

Algorithm

intervals

Results

729.0ms	2297×	body	1280	valid
354.0ms	1663×	body	640	valid
127.0ms	2864×	body	80	valid
116.0ms	802×	body	320	valid
105.0ms	2519×	body	80	overflowed
40.0ms	423×	body	160	valid

Details

sample67.0ms

simplify870.0ms

prune5.0ms

localize11.0ms

rewrite37.0ms

series36.0ms

simplify681.0ms

prune259.0ms

localize14.0ms

rewrite54.0ms

series31.0ms

simplify537.0ms

prune504.0ms

localize17.0ms

rewrite51.0ms

series41.0ms

simplify980.0ms

prune373.0ms

localize18.0ms

rewrite67.0ms

series38.0ms

simplify793.0ms

prune532.0ms

regimes48.0ms

bsearch20.0ms

simplify3.0ms

end0.0ms

sample1.7s

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