Details

sample447.0ms

Algorithm

intervals

Results

180.0ms	206×	body	10240	exit
57.0ms	406×	body	80	nan
48.0ms	236×	body	80	valid
4.0ms	23×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4825
7	1216
6	342
5	135
4	66
3	38
2	27
1	19
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

localize36.0ms

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))
4.0b	(- (exp (* 2.0 x)) 1.0)
4.2b	(- (exp x) 1.0)

rewrite144.0ms

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-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 155

Calls

4 calls:

23.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
31.0ms	(- (exp (* 2.0 x)) 1.0)
21.0ms	(- (exp x) 1.0)

series683.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
104.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)
434.0ms	(- (exp x) 1.0)

simplify2.5s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
3	4025
2	1183
1	501
0	232

prune796.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(sqrt (exp (* 2.0 x)))
4.2b	(- (exp x) 1.0)
4.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt` `sqrt-prod`
45×	`*-un-lft-identity` `prod-diff`
39×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
6×	`pow1` `sqrt-pow1`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`rem-sqrt-square` `exp-prod` `sub-neg` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 124

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
2.0ms	(sqrt (exp (* 2.0 x)))
13.0ms	(- (exp x) 1.0)
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series142.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (exp (* 2.0 x)))
31.0ms	(sqrt (exp (* 2.0 x)))
15.0ms	(- (exp x) 1.0)
64.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify2.5s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
3	2160
2	771
1	352
0	162

prune568.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
0.0b	(sqrt (exp (* 2.0 x)))
4.2b	(- (exp x) 1.0)
4.2b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
51×	`prod-diff`
50×	`*-un-lft-identity`
42×	`add-cube-cbrt`
32×	`sqrt-prod`
23×	`unpow-prod-down`
11×	`add-log-exp`
10×	`fma-neg`
9×	`sqr-pow`
7×	`difference-of-squares`
6×	`fma-def`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `sum-log` `flip3-+` `exp-to-pow` `pow1/2` `flip-+`

Counts

4 → 136

Calls

4 calls:

12.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.0ms	(sqrt (exp (* 2.0 x)))
9.0ms	(- (exp x) 1.0)
23.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

series209.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
46.0ms	(sqrt (exp (* 2.0 x)))
29.0ms	(- (exp x) 1.0)
73.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

simplify2.9s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
3	3371
2	1178
1	484
0	216

prune930.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
0.0b	(sqrt (exp (* 2.0 x)))
4.2b	(- (exp x) 1.0)
4.2b	(- (exp (* 1.0 x)) (sqrt 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
27×	`prod-diff` `add-cube-cbrt`
18×	`sqrt-prod`
11×	`add-log-exp`
6×	`fma-def` `fma-neg`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sqrt-pow1` `difference-of-squares`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `sum-log` `flip3-+` `exp-to-pow` `pow1/2` `flip-+`

Counts

4 → 104

Calls

4 calls:

15.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.0ms	(sqrt (exp (* 2.0 x)))
16.0ms	(- (exp x) 1.0)
20.0ms	(- (exp (* 1.0 x)) (sqrt 1.0))

series177.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
28.0ms	(sqrt (exp (* 2.0 x)))
18.0ms	(- (exp x) 1.0)
59.0ms	(- (exp (* 1.0 x)) (sqrt 1.0))

simplify2.8s

Counts

116 → 116

Iterations

Iter	Nodes
done	5016
3	2847
2	956
1	408
0	180

prune646.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

regimes78.0ms

Accuracy

74.1% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.7b

bsearch74.0ms

Steps

Iters	Range		Point
7	-2.5598413051174652e-12	-4.218890414275596e-14	-8.655783571717727e-13

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.7s	6715×	body	10240	exit
1.3s	12553×	body	80	nan
597.0ms	7413×	body	80	valid
148.0ms	715×	body	160	valid