Details

sample230.0ms

Algorithm

intervals

Results

108.0ms	204×	body	10240	exit
24.0ms	388×	body	80	nan
16.0ms	242×	body	80	valid
2.0ms	20×	body	160	valid

simplify2.8s

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	181	12
6	489	12
7	1695	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize13.0ms

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)))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp x) 1.0)

rewrite164.0ms

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:

70.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
48.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
19.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

series387.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
181.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
47.0ms	(- (exp (* 2.0 x)) 1.0)
41.0ms	(- (exp x) 1.0)

simplify2.5s

Counts

167 → 167

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1074	2471
3	3564	2362
done	5000	2357

prune651.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.2b	(sqrt (+ (exp x) 1.0))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`times-frac`
21×	`difference-of-squares`
13×	`prod-diff`
9×	`exp-sum`
8×	`add-log-exp`
7×	`fma-neg` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `flip3--` `sqrt-prod` `flip--` `log1p-expm1-u`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `clear-num` `flip-+` `hypot-def` `div-inv` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

124.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
25.0ms	(sqrt (+ (exp x) 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)
111.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series402.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
42.0ms	(sqrt (+ (exp x) 1.0))
60.0ms	(- (exp (* 2.0 x)) 1.0)
35.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.2s

Counts

137 → 137

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	223	2351
1	508	2210
2	1366	1996
done	5000	1944

prune748.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.3b	(sqrt (exp x))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`times-frac`
21×	`difference-of-squares`
13×	`prod-diff`
9×	`exp-sum`
8×	`add-log-exp`
7×	`fma-neg` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `flip--` `log1p-expm1-u`
3×	`exp-prod` `sqrt-prod`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

135.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
6.0ms	(sqrt (exp x))
29.0ms	(- (exp (* 2.0 x)) 1.0)
83.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series342.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
21.0ms	(sqrt (exp x))
36.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify3.2s

Counts

136 → 136

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	209	2258
1	465	2125
2	1132	1916
3	4318	1819
done	5000	1817

prune946.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`prod-diff`
8×	`add-log-exp`
7×	`fma-neg`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--`
1×	`distribute-lft-out--`

Counts

4 → 78

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
31.0ms	(- (exp (* 2.0 x)) 1.0)
106.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series632.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt x)
275.0ms	(cbrt x)
32.0ms	(- (exp (* 2.0 x)) 1.0)
41.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.7s

Counts

90 → 90

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	138	943
1	289	835
2	672	706
3	2310	641
done	5001	593

prune545.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes42.0ms

Accuracy

75.5% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.1b

bsearch93.0ms

Steps

Iters	Range		Point
8	-1.5271913101819107e-13	-4.24910696022173e-16	-9.48316931979068e-14

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	55
1	37	55
done	37	55

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.9s	6588×	body	10240	exit
1.0s	12585×	body	80	nan
509.0ms	7352×	body	80	valid
121.0ms	757×	body	160	valid