Details

sample387.0ms

Algorithm

intervals

Results

51.0ms	175×	body	10240	exit
11.0ms	388×	body	80	nan
9.0ms	244×	body	80	valid
1.0ms	16×	body	160	valid

simplify72.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7
done	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.5b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.1b	(- (exp x) 1.0)

rewrite115.0ms

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:

29.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
48.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
16.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series200.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify53.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470
done	5001	1470

prune384.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.5b	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
3.0b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.0b	(- (exp (* 2.0 x)) 1.0)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`sqrt-div` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`frac-times` `flip3--` `sqrt-pow1` `flip3-+` `associate-*r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 96

Calls

4 calls:

19.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
32.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
15.0ms	(- (exp (* 2.0 x)) 1.0)

series415.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
189.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify52.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	439	1178
1	1619	1042
2	5003	1028
done	5003	1028

prune341.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.2b	(sqrt (* 1.0 (+ (exp x) 1.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

9.0ms	(+ (exp x) 1.0)
13.0ms	(sqrt (* 1.0 (+ (exp x) 1.0)))

series82.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(+ (exp x) 1.0)
73.0ms	(sqrt (* 1.0 (+ (exp x) 1.0)))

simplify45.0ms

Counts

38 → 38

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	169	181
1	471	171
2	1575	165
3	5002	164
done	5002	164

prune92.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
0.2b	(sqrt (exp x))
0.2b	(sqrt (exp x))
0.2b	(sqrt (* 1.0 (fma (sqrt (exp x)) (sqrt (exp x)) 1.0)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `sqrt-pow1`
9×	`pow1`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`sqrt-prod`
6×	`exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
3.0ms	(sqrt (exp x))
3.0ms	(sqrt (exp x))
5.0ms	(sqrt (* 1.0 (fma (sqrt (exp x)) (sqrt (exp x)) 1.0)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
12.0ms	(sqrt (exp x))
12.0ms	(sqrt (exp x))
104.0ms	(sqrt (* 1.0 (fma (sqrt (exp x)) (sqrt (exp x)) 1.0)))

simplify41.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	139	316
1	369	291
2	1353	285
3	5001	281
done	5001	281

prune174.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes18.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7
done	8	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6666×	body	10240	exit
381.0ms	12737×	body	80	nan
231.0ms	7414×	body	80	valid
54.0ms	728×	body	160	valid