Details

sample222.0ms

Algorithm

intervals

Results

92.0ms	202×	body	10240	exit
19.0ms	410×	body	80	nan
11.0ms	230×	body	80	valid
3.0ms	29×	body	160	valid

simplify1.0s

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize27.0ms

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))
5.6b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite144.0ms

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:

36.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
70.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
14.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series286.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
67.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
35.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify1.5s

Counts: 135 → 135

prune542.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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)))
5.0ms	(sqrt (exp (* 2.0 x)))
20.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
24.0ms	(- (exp x) 1.0)

series155.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (exp (* 2.0 x)))
23.0ms	(sqrt (exp (* 2.0 x)))
79.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
21.0ms	(- (exp x) 1.0)

simplify1.5s

Counts: 74 → 74

prune280.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize37.0ms

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

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

83×	`sqrt-pow1`
75×	`sqrt-prod`
58×	`add-sqr-sqrt`
28×	`pow1`
23×	`*-un-lft-identity`
21×	`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`
6×	`add-exp-log` `add-cbrt-cube`
5×	`difference-of-squares`
3×	`distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
63.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
34.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
19.0ms	(- (exp x) 1.0)

series143.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (exp (* 2.0 x)))
30.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
64.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

simplify662.0ms

Counts: 146 → 146

prune541.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (sqrt (exp (* 2.0 x))) 3))
0.1b	(pow (sqrt (exp (* 2.0 x))) 3)
5.8b	(- (cbrt (pow (sqrt (exp (* 2.0 x))) 3)) (sqrt 1.0))
5.8b	(- (exp x) 1.0)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
30×	`cbrt-prod`
23×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`unpow-prod-down` `cube-prod`
15×	`difference-of-squares`
14×	`add-cube-cbrt`
9×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `pow-pow` `add-cbrt-cube`
4×	`sqr-pow`
3×	`pow-unpow` `sqrt-pow1`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out--`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 102

Calls

4 calls:

6.0ms	(cbrt (pow (sqrt (exp (* 2.0 x))) 3))
7.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
78.0ms	(- (cbrt (pow (sqrt (exp (* 2.0 x))) 3)) (sqrt 1.0))
21.0ms	(- (exp x) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(cbrt (pow (sqrt (exp (* 2.0 x))) 3))
92.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
81.0ms	(- (cbrt (pow (sqrt (exp (* 2.0 x))) 3)) (sqrt 1.0))
24.0ms	(- (exp x) 1.0)

simplify601.0ms

Counts: 114 → 114

prune489.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes72.0ms

Accuracy

87.3% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 3.8b

bsearch151.0ms

Steps

Iters	Range		Point
7	1.9251139816623773e-14	3.914952597617144e-13	3.189879657056316e-14
8	-2.2652292653064335e-05	-5.584316466887409e-09	-1.7294351212985426e-05

simplify1.5s

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.8s	6750×	body	10240	exit
2.2s	12663×	body	80	nan
580.0ms	7344×	body	80	valid
164.0ms	768×	body	160	valid