Details

sample72.0ms

Algorithm

intervals

Results

27.0ms	84×	body	1280	valid
9.0ms	41×	body	640	valid
8.0ms	171×	body	80	valid
4.0ms	24×	body	320	valid
2.0ms	15×	body	160	valid

simplify151.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize12.0ms

Local error

Found 1 expressions with local error:

4.1b	(- (exp (* a x)) 1.0)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

24.0ms

(- (exp (* a x)) 1.0)

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(- (exp (* a x)) 1.0)

simplify93.0ms

Counts: 17 → 17

prune80.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
0.0b	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
0.0b	(pow (exp (* a x)) 3)
4.0b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
9×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `pow-pow` `associate-/r*`
2×	`associate-+l+` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `rem-cube-cbrt`

Counts

4 → 192

Calls

4 calls:

168.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
30.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
12.0ms	(pow (exp (* a x)) 3)
36.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series342.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
56.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
31.0ms	(pow (exp (* a x)) 3)
94.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify123.0ms

Counts: 204 → 204

prune713.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
0.0b	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
0.2b	(* (* a x) 3)
4.0b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
33×	`times-frac`
31×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`difference-of-squares`
15×	`difference-cubes`
13×	`add-log-exp`
11×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`pow1`
5×	`unpow-prod-down` `exp-lft-cube` `exp-prod` `exp-to-pow` `cube-prod` `distribute-lft-out--` `sqr-pow`
3×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`associate-+l+` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `div-exp` `associate-l` `clear-num` `sum-log` `*-commutative` `div-inv`

Counts

4 → 115

Calls

4 calls:

129.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
47.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
36.0ms	(* (* a x) 3)
34.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series318.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
67.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
36.0ms	(* (* a x) 3)
59.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify107.0ms

Counts: 127 → 127

prune607.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp (* a x)) 1.0) (+ (exp (* a x)) 1.0))
0.0b	(pow (* (exp (* a x)) (+ (exp (* a x)) 1.0)) 3)
0.2b	(* (* a x) 3)
4.0b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
19×	`pow1` `add-sqr-sqrt`
14×	`add-cbrt-cube`
13×	`add-exp-log`
10×	`add-cube-cbrt`
7×	`flip3-+` `associate-r` `flip-+` `add-log-exp`
6×	`swap-sqr` `distribute-lft-out`
5×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`frac-times` `associate-*r/` `difference-of-squares`
3×	`difference-cubes` `pow-unpow`
2×	`cube-div` `unpow-prod-down` `pow-pow` `cube-prod` `associate-l/` `pow-exp` `-commutative` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `exp-lft-cube` `exp-prod` `flip3--` `exp-to-pow` `distribute-lft-in` `pow-plus` `diff-log` `unpow3` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

123.0ms	(* (+ (exp (* a x)) 1.0) (+ (exp (* a x)) 1.0))
20.0ms	(pow (* (exp (* a x)) (+ (exp (* a x)) 1.0)) 3)
30.0ms	(* (* a x) 3)
24.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series211.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ (exp (* a x)) 1.0) (+ (exp (* a x)) 1.0))
71.0ms	(pow (* (exp (* a x)) (+ (exp (* a x)) 1.0)) 3)
22.0ms	(* (* a x) 3)
73.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify113.0ms

Counts: 114 → 114

prune608.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

regimes263.0ms

Accuracy

94.4% (1.2b remaining)

Error of 9.5b against oracle of 8.3b and baseline of 29.5b

bsearch2.0ms

simplify91.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

713.0ms	2682×	body	1280	valid
280.0ms	5497×	body	80	valid
277.0ms	1300×	body	640	valid
131.0ms	802×	body	320	valid
27.0ms	382×	body	160	valid