Details

sample340.0ms

Algorithm

intervals

Results

120.0ms	229×	body	10240	exit
75.0ms	236×	body	80	valid
29.0ms	400×	body	80	nan
5.0ms	25×	body	160	valid

simplify960.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.3b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp x) 1.0)

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
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 → 123

Calls

4 calls:

37.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
20.0ms	(- (exp (* 2.0 x)) 1.0)
57.0ms	(- (exp x) 1.0)

series252.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
70.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
42.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp x) 1.0)

simplify1.5s

Counts: 135 → 135

prune526.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(sqrt (exp (* 2.0 x)))
5.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.4b	(- (exp x) 1.0)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-pow1`
5×	`difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

4.0ms	(sqrt (exp (* 2.0 x)))
3.0ms	(sqrt (exp (* 2.0 x)))
18.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
12.0ms	(- (exp x) 1.0)

series184.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (exp (* 2.0 x)))
30.0ms	(sqrt (exp (* 2.0 x)))
87.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
34.0ms	(- (exp x) 1.0)

simplify1.4s

Counts: 74 → 74

prune284.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize24.0ms

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)))
5.4b	(- (exp x) 1.0)
5.4b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-log-exp`
8×	`sqrt-prod`
7×	`difference-of-squares`
5×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`sub-neg` `unpow-prod-down` `flip3--` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--` `sqr-pow`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `exp-to-pow` `flip3-+` `pow1/2` `sum-log` `flip-+`

Counts

4 → 61

Calls

4 calls:

34.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.0ms	(sqrt (exp (* 2.0 x)))
10.0ms	(- (exp x) 1.0)
32.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

series209.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
23.0ms	(sqrt (exp (* 2.0 x)))
23.0ms	(- (exp x) 1.0)
92.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

simplify896.0ms

Counts: 73 → 73

prune426.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.1b	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
5.4b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
5.4b	(- (exp x) 1.0)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

83×	`sqrt-pow1`
72×	`sqrt-prod`
60×	`add-sqr-sqrt`
28×	`pow1`
21×	`*-un-lft-identity` `add-log-exp`
17×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
13×	`exp-prod` `exp-to-pow` `pow-prod-up`
9×	`associate-r` `associate-l` `pow-prod-down` `pow-sqr` `unswap-sqr`
7×	`difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
2×	`sub-neg` `unpow-prod-down` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `sqr-pow`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 135

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
41.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
48.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
21.0ms	(- (exp x) 1.0)

series161.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (exp (* 2.0 x)))
32.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
82.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

simplify809.0ms

Counts: 147 → 147

prune640.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes34.0ms

Accuracy

99.6% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 3.0b

bsearch159.0ms

Steps

Iters	Range		Point
8	1.2037210016196379e-18	3.5562758402477077e-16	1.1250860145338832e-16
6	-1.3250394268561034e-11	-3.014080757910363e-12	-1.115913044114018e-11

simplify2.4s

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.7s	6572×	body	10240	exit
911.0ms	12400×	body	80	nan
633.0ms	7395×	body	80	valid
609.0ms	731×	body	160	valid