Details

sample242.0ms

Algorithm

intervals

Results

92.0ms	194×	body	10240	exit
18.0ms	433×	body	80	nan
13.0ms	240×	body	80	valid
2.0ms	23×	body	160	valid

simplify994.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	767
5	185
4	76
3	41
2	28
1	19
0	10

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.3b	(- (exp x) 1.0)

rewrite139.0ms

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:

44.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
40.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
22.0ms	(- (exp (* 2.0 x)) 1.0)
21.0ms	(- (exp x) 1.0)

series296.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
79.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
54.0ms	(- (exp (* 2.0 x)) 1.0)
44.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
2	1528
1	502
0	232

prune816.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
4.3b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.3b	(- (exp (* 2.0 x)) 1.0)

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
171×	`*-un-lft-identity`
127×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`fma-neg`
2×	`clear-num` `frac-2neg` `flip3--` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 206

Calls

4 calls:

17.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
74.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
17.0ms	(- (exp (* 2.0 x)) 1.0)

series361.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
169.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
63.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
37.0ms	(- (exp (* 2.0 x)) 1.0)

simplify1.7s

Counts

218 → 218

Iterations

Iter	Nodes
done	5000
2	4247
1	887
0	304

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (* 2.0 x)) 1.0) (* (/ (fma 1.0 (- 1.0) (exp (* 2 x))) (+ (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
4.3b	(fma 1.0 (- 1.0) (exp (* 2 x)))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.3b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`prod-diff`
8×	`add-log-exp`
5×	`times-frac` `associate-/r/` `associate-/l*`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `fma-neg` `div-exp` `log1p-expm1-u`
3×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`frac-times` `sub-neg` `flip3-+` `diff-log` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `distribute-rgt-out--` `div-sub` `associate-l/` `fma-udef` `div-inv`

Counts

4 → 92

Calls

4 calls:

99.0ms	(/ (- (exp (* 2.0 x)) 1.0) (* (/ (fma 1.0 (- 1.0) (exp (* 2 x))) (+ (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
0.0ms	(fma 1.0 (- 1.0) (exp (* 2 x)))
23.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series523.0ms

Counts

4 → 12

Calls

4 calls:

392.0ms	(/ (- (exp (* 2.0 x)) 1.0) (* (/ (fma 1.0 (- 1.0) (exp (* 2 x))) (+ (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
64.0ms	(fma 1.0 (- 1.0) (exp (* 2 x)))
33.0ms	(- (exp (* 2.0 x)) 1.0)
34.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	3612
1	658
0	210

prune799.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0))
0.2b	(* (/ (* x x) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (* x x) (sqrt 2.0))
0.5b	(/ x (sqrt 2.0))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
95×	`add-cube-cbrt`
87×	`times-frac`
78×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
22×	`sqrt-prod`
20×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
10×	`associate-l`
9×	`div-inv`
6×	`pow1` `associate-r`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `flip3--` `associate-*r/` `flip--` `difference-of-squares`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef` `distribute-lft-out--`

Counts

4 → 203

Calls

4 calls:

0.0ms	(fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0))
96.0ms	(* (/ (* x x) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
21.0ms	(/ (* x x) (sqrt 2.0))
10.0ms	(/ x (sqrt 2.0))

series455.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(fma 0.5 (/ x (sqrt 2.0)) (sqrt 2.0))
115.0ms	(* (/ (* x x) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
77.0ms	(/ (* x x) (sqrt 2.0))
87.0ms	(/ x (sqrt 2.0))

simplify666.0ms

Counts

215 → 215

Iterations

Iter	Nodes
done	5000
1	1181
0	394

prune766.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes67.0ms

Accuracy

75.6% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.9b

bsearch38.0ms

Steps

Iters	Range		Point
5	-6.8406817238881764e-12	-3.323511487531625e-12	-6.780812387076979e-12

simplify5.0ms

Iterations

Iter	Nodes
done	36
1	36
0	32

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.8s	6720×	body	10240	exit
945.0ms	12340×	body	80	nan
802.0ms	7398×	body	80	valid
117.0ms	753×	body	160	valid