Details

sample230.0ms

Algorithm

intervals

Results

53.0ms	175×	body	10240	exit
18.0ms	388×	body	80	nan
14.0ms	244×	body	80	valid
2.0ms	16×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 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)

rewrite158.0ms

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:

35.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
80.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
14.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series309.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
102.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
43.0ms	(- (exp (* 2.0 x)) 1.0)
43.0ms	(- (exp x) 1.0)

simplify2.6s

Counts

167 → 167

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1071	2471
3	3554	2362
done	5000	2356

prune529.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

60.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
141.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
29.0ms	(- (exp (* 2.0 x)) 1.0)
90.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series479.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
237.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
26.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.5s

Counts

136 → 136

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	235	2675
1	562	2520
2	1613	2290
done	5001	2150

prune581.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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:

19.0ms	(+ (exp x) 1.0)
12.0ms	(sqrt (* 1.0 (+ (exp x) 1.0)))

series99.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(+ (exp x) 1.0)
85.0ms	(sqrt (* 1.0 (+ (exp x) 1.0)))

simplify3.3s

Counts

38 → 38

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	71	331
1	170	306
2	447	290
3	1256	281
4	4650	277
done	5000	276

prune100.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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)))

rewrite14.0ms

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))
6.0ms	(sqrt (* 1.0 (fma (sqrt (exp x)) (sqrt (exp x)) 1.0)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
23.0ms	(sqrt (exp x))
23.0ms	(sqrt (exp x))
141.0ms	(sqrt (* 1.0 (fma (sqrt (exp x)) (sqrt (exp x)) 1.0)))

simplify2.9s

Counts

71 → 71

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	78	558
1	140	409
2	329	394
3	1015	385
4	3897	377
done	5000	377

prune240.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
done	8	11

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.8s	6666×	body	10240	exit
539.0ms	12737×	body	80	nan
349.0ms	7414×	body	80	valid
78.0ms	728×	body	160	valid