Details

sample300.0ms

Algorithm

intervals

Results

100.0ms	247×	body	10240	exit
56.0ms	230×	body	80	valid
28.0ms	476×	body	80	nan
4.0ms	28×	body	160	valid

simplify9.8s

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize68.0ms

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))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite215.0ms

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/` `insert-posit16` `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 → 159

Calls

4 calls:

51.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
83.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

series419.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
139.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
42.0ms	(- (exp (* 2.0 x)) 1.0)
60.0ms	(- (exp x) 1.0)

simplify6.3s

Counts

171 → 171

Iterations

Iter	Nodes
done	5000
3	4084
2	1179
1	505
0	236

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
0.1b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
5.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.8b	(- (exp x) 1.0)

rewrite498.0ms

Algorithm

rewrite-expression-head

Rules

125×	`sqrt-prod`
117×	`prod-diff`
113×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
89×	`add-cube-cbrt`
38×	`distribute-rgt-in` `distribute-lft-in`
11×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
9×	`flip3--` `fma-neg` `associate-r` `flip--`
8×	`frac-times` `add-log-exp` `associate-/l/`
7×	`distribute-lft-out--`
6×	`pow1` `flip3-+` `flip-+`
5×	`associate-/r` `times-frac` `associate-l*`
4×	`expm1-log1p-u` `sub-neg` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 243

Calls

4 calls:

152.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
257.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
42.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (exp x) 1.0)

series686.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
206.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
97.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
33.0ms	(- (exp x) 1.0)

simplify6.2s

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
2	3377
1	992
0	327

prune2.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
5.8b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
5.8b	(- (exp x) 1.0)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
31×	`times-frac`
30×	`add-cube-cbrt`
21×	`sqrt-prod`
9×	`prod-diff`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--` `associate-/l*`
2×	`rem-sqrt-square` `div-inv`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-exp` `fma-udef`

Counts

4 → 116

Calls

4 calls:

25.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
33.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
1.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
18.0ms	(- (exp x) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

734.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
230.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
177.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
30.0ms	(- (exp x) 1.0)

simplify5.7s

Counts

128 → 128

Iterations

Iter	Nodes
done	5037
3	3306
2	932
1	373
0	197

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x (fma 0.4999999999999998 x 1.0) 2.0)
26.0b	(sqrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
2×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

2 → 27

Calls

2 calls:

2.0ms	(fma x (fma 0.4999999999999998 x 1.0) 2.0)
6.0ms	(sqrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

series172.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(fma x (fma 0.4999999999999998 x 1.0) 2.0)
138.0ms	(sqrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

simplify3.1s

Counts

33 → 33

Iterations

Iter	Nodes
done	5000
3	1449
2	423
1	149
0	67

prune349.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes137.0ms

Accuracy

74.3% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.2b

bsearch56.0ms

Steps

Iters	Range		Point
7	-4.6430296561414034e-09	-1.8758842618254644e-11	-4.527236342338421e-09

simplify17.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.5s	6791×	body	10240	exit
995.0ms	12669×	body	80	nan
937.0ms	7438×	body	80	valid
105.0ms	684×	body	160	valid