Details

sample57.0ms

Algorithm

intervals

Results

21.0ms	86×	body	1280	valid
12.0ms	36×	body	640	valid
6.0ms	190×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify134.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize5.0ms

Local error

Found 1 expressions with local error:

2.8b	(- (exp (* a x)) 1.0)

rewrite14.0ms

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:

13.0ms

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

series43.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

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

simplify108.0ms

Counts: 17 → 17

prune113.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.5b

localize9.0ms

Local error

Found 2 expressions with local error:

2.8b	(log (exp (- (exp (* a x)) 1.0)))
2.8b	(- (exp (* a x)) 1.0)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`log-pow`
5×	`log-prod` `exp-prod`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1`
2×	`add-exp-log` `sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 34

Calls

2 calls:

45.0ms	(log (exp (- (exp (* a x)) 1.0)))
19.0ms	(- (exp (* a x)) 1.0)

series89.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(log (exp (- (exp (* a x)) 1.0)))
42.0ms	(- (exp (* a x)) 1.0)

simplify98.0ms

Counts: 40 → 40

prune161.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
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	(pow (exp (* a x)) 3)
2.7b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite265.0ms

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:

24.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
155.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
16.0ms	(pow (exp (* a x)) 3)
60.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series352.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
137.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
51.0ms	(pow (exp (* a x)) 3)
82.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify100.0ms

Counts: 204 → 204

prune641.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
0.0b	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
0.2b	(* (* a x) 3)
2.7b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite182.0ms

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:

33.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
104.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
18.0ms	(* (* a x) 3)
18.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series308.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
145.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
39.0ms	(* (* a x) 3)
60.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify86.0ms

Counts: 127 → 127

prune572.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.5b

regimes327.0ms

Accuracy

93.7% (1.3b remaining)

Error of 9.4b against oracle of 8.1b and baseline of 28.9b

bsearch1.0ms

simplify81.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

900.0ms	2727×	body	1280	valid
248.0ms	5596×	body	80	valid
235.0ms	1276×	body	640	valid
166.0ms	744×	body	320	valid
36.0ms	390×	body	160	valid