Details

sample454.0ms

Algorithm

intervals

Results

162.0ms	204×	body	10240	exit
57.0ms	364×	body	80	nan
20.0ms	238×	body	80	valid
3.0ms	22×	body	160	valid

simplify3.0s

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: 3.9b

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))
4.4b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp x) 1.0)

rewrite153.0ms

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:

47.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
54.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
29.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

series344.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
109.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
43.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

167 → 167

Iterations

Useful iterations: done (2.4s)

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

prune545.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
4.4b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`prod-diff`
10×	`add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `flip3-+` `sqrt-div` `diff-log` `flip--` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

28.0ms	(sqrt (+ (exp x) 1.0))
20.0ms	(+ (exp x) 1.0)
30.0ms	(- (exp (* 2.0 x)) 1.0)
88.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series125.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sqrt (+ (exp x) 1.0))
9.0ms	(+ (exp x) 1.0)
26.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.3s

Counts

100 → 100

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	166	1120
1	362	992
2	908	860
3	3265	761
done	5000	757

prune553.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt (exp x)) (sqrt 1.0))
0.0b	(sqrt (exp x))
4.4b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

1.0ms	(hypot (sqrt (exp x)) (sqrt 1.0))
7.0ms	(sqrt (exp x))
21.0ms	(- (exp (* 2.0 x)) 1.0)
116.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series310.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(hypot (sqrt (exp x)) (sqrt 1.0))
13.0ms	(sqrt (exp x))
39.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.2s

Counts

92 → 92

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	172	1073
1	348	931
2	804	800
3	2782	701
done	5001	683

prune521.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (/ x (sqrt 2.0)) 0.5 (sqrt 2.0))
0.1b	(fma (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)) (fma (/ x (sqrt 2.0)) 0.5 (sqrt 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
51×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`sqrt-prod`
21×	`unpow-prod-down`
12×	`associate-/r*`
11×	`add-exp-log` `associate-/l*`
8×	`add-cbrt-cube`
7×	`unpow2` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `fma-udef` `div-inv`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 139

Calls

4 calls:

5.0ms	(fma (/ x (sqrt 2.0)) 0.5 (sqrt 2.0))
0.0ms	(fma (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)) (fma (/ x (sqrt 2.0)) 0.5 (sqrt 2.0)))
11.0ms	(/ (pow x 2) (sqrt 2.0))
7.0ms	(/ x (sqrt 2.0))

series546.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(fma (/ x (sqrt 2.0)) 0.5 (sqrt 2.0))
161.0ms	(fma (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)) (fma (/ x (sqrt 2.0)) 0.5 (sqrt 2.0)))
108.0ms	(/ (pow x 2) (sqrt 2.0))
91.0ms	(/ x (sqrt 2.0))

simplify1.9s

Counts

151 → 151

Iterations

Useful iterations: 3 (768.0ms)

Iter	Nodes	Cost
0	192	1873
1	307	1694
2	685	1511
3	2346	1507
done	5001	1507

prune475.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes34.0ms

Accuracy

76.4% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.8b

bsearch107.0ms

Steps

Iters	Range		Point
8	-8.074815721195404e-17	-5.960240395557237e-20	-5.5218505216622935e-17

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	47
1	34	47
done	34	47

end0.0ms

sample7.5s

Algorithm

intervals

Results

5.2s	6749×	body	10240	exit
949.0ms	12721×	body	80	nan
590.0ms	7390×	body	80	valid
173.0ms	746×	body	160	valid