Details

sample329.0ms

Algorithm

intervals

Results

43.0ms	195×	body	10240	exit
12.0ms	351×	body	80	nan
9.0ms	233×	body	80	valid
2.0ms	24×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	175	12
6	476	12
7	1519	12
done	5001	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.8b	(- (exp (* 2.0 x)) 1.0)
5.0b	(- (exp x) 1.0)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
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 → 155

Calls

4 calls:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp x) 1.0)

series198.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

167 → 167

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	232	2954
1	475	2688
2	1077	2471
3	3777	2398
done	5000	2396

prune408.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
239×	`*-un-lft-identity`
197×	`add-sqr-sqrt`
111×	`add-cube-cbrt`
88×	`difference-of-squares`
36×	`distribute-lft-out`
32×	`exp-sum`
30×	`associate-/r*`
28×	`distribute-lft-out--`
15×	`associate-/r/`
13×	`prod-diff`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `fma-neg` `flip-+`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 281

Calls

4 calls:

65.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
53.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series178.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
91.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.3s

Counts

293 → 293

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	399	8480
1	1118	8124
2	3796	7676
done	5000	7663

prune869.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))) 3)
0.1b	(cbrt (pow (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))) 3))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

920×	`times-frac`
733×	`*-un-lft-identity`
614×	`add-sqr-sqrt`
323×	`add-cube-cbrt`
276×	`cbrt-prod`
270×	`unpow-prod-down` `cube-prod`
267×	`difference-of-squares`
105×	`distribute-lft-out--`
100×	`distribute-lft-out`
83×	`exp-sum`
44×	`associate-/r/`
24×	`div-inv`
20×	`flip3-+` `flip-+`
13×	`prod-diff`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `pow-exp` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube`

Counts

4 → 634

Calls

4 calls:

66.0ms	(pow (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))) 3)
73.0ms	(cbrt (pow (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))) 3))
5.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series264.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(pow (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))) 3)
90.0ms	(cbrt (pow (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))) 3))
25.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify755.0ms

Counts

646 → 646

Iterations

Useful iterations: done (712.0ms)

Iter	Nodes	Cost
0	723	27011
1	2339	24368
done	5000	24224

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp (+ x x)) (* 1.0 1.0))
4.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `prod-diff`
22×	`add-cube-cbrt`
14×	`fma-neg`
12×	`add-log-exp`
6×	`exp-sum` `difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`distribute-lft-out--`

Counts

4 → 104

Calls

4 calls:

5.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series91.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (exp (* 2.0 x)) 1.0)
28.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.2s

Counts

116 → 116

Iterations

Useful iterations: 3 (343.0ms)

Iter	Nodes	Cost
0	114	1602
1	247	1402
2	617	1164
3	2214	1050
done	5000	1050

prune552.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

75.7% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.9b

bsearch27.0ms

Steps

Iters	Range		Point
5	-8.78551315505774e-06	-2.7321346469351546e-06	-8.580579348341847e-06

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	26	35
done	26	35

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	6724×	body	10240	exit
426.0ms	12569×	body	80	nan
262.0ms	7366×	body	80	valid
61.0ms	738×	body	160	valid