Details

sample56.0ms

Algorithm

intervals

Results

22.0ms	68×	body	1280	valid
10.0ms	42×	body	640	valid
8.0ms	170×	body	80	valid
4.0ms	31×	body	320	valid
2.0ms	18×	body	160	valid

simplify16.0ms

Calls

1 calls:

Slowest

16.0ms

(- (exp (* a x)) 1)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize8.0ms

Local error

Found 2 expressions with local error:

4.7b	(- (exp (* a x)) 1)
0.1b	(exp (* a x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `add-log-exp`
2×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`exp-prod` `sub-neg` `flip3--` `difference-of-sqr-1` `flip--` `rem-exp-log`

Calls

2 calls:

Slowest

5.0ms	(- (exp (* a x)) 1)
1.0ms	(exp (* a x))

series61.0ms

Calls

2 calls:

Slowest

47.0ms	(- (exp (* a x)) 1)
15.0ms	(exp (* a x))

simplify353.0ms

Calls

9 calls:

Slowest

144.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
127.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
21.0ms	(- (exp (* a x)) 1)
19.0ms	(+ (sqrt (exp (* a x))) 1)
18.0ms	(- (exp (* a x)) 1)

prune180.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

12.8b	(+ (+ (* a x) (* 1/6 (* (* (* a x) (* a x)) (* a x)))) (* 1/2 (* (* a x) (* a x))))
0.2b	(* (* a x) (* a x))
0.2b	(* (* a x) (* a x))
0.1b	(* 1/6 (* (* (* a x) (* a x)) (* a x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16`
3×	`sum-log` `associate-r` `*-commutative`
2×	`pow2` `pow-plus` `associate-l` `pow-prod-down` `prod-exp` `pow-prod-up` `cbrt-unprod`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Calls

4 calls:

Slowest

29.0ms	(+ (+ (* a x) (* 1/6 (* (* (* a x) (* a x)) (* a x)))) (* 1/2 (* (* a x) (* a x))))
21.0ms	(* 1/6 (* (* (* a x) (* a x)) (* a x)))
8.0ms	(* (* a x) (* a x))
8.0ms	(* (* a x) (* a x))

series144.0ms

Calls

4 calls:

Slowest

75.0ms	(+ (+ (* a x) (* 1/6 (* (* (* a x) (* a x)) (* a x)))) (* 1/2 (* (* a x) (* a x))))
36.0ms	(* 1/6 (* (* (* a x) (* a x)) (* a x)))
16.0ms	(* (* a x) (* a x))
16.0ms	(* (* a x) (* a x))

simplify2.1s

Calls

28 calls:

Slowest

293.0ms	(* (exp (+ (* a x) (* 1/6 (* (* (* a x) (* a x)) (* a x))))) (exp (* 1/2 (* (* a x) (* a x)))))
237.0ms	(* (* (exp (* a x)) (exp (* 1/6 (* (* (* a x) (* a x)) (* a x))))) (exp (* 1/2 (* (* a x) (* a x)))))
221.0ms	(* (* (* (* a x) (* a x)) (* a x)) (* (* (* a x) (* a x)) (* a x)))
207.0ms	(* 1/6 (* (pow a 3) (pow x 3)))
202.0ms	(* (* (* (* a x) (* a x)) (* a x)) (* (* (* a x) (* a x)) (* a x)))

prune563.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

4.7b	(- (exp (* a x)) 1)
4.7b	(- (exp (* a x)) 1)
4.7b	(- (exp (* a x)) 1)
0.1b	(exp (* a x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`add-log-exp`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`sub-neg` `flip3--` `difference-of-sqr-1` `flip--`
1×	`exp-prod` `rem-exp-log`

Calls

4 calls:

Slowest

11.0ms	(- (exp (* a x)) 1)
10.0ms	(- (exp (* a x)) 1)
10.0ms	(- (exp (* a x)) 1)
2.0ms	(exp (* a x))

series119.0ms

Calls

4 calls:

Slowest

43.0ms	(- (exp (* a x)) 1)
35.0ms	(- (exp (* a x)) 1)
30.0ms	(- (exp (* a x)) 1)
11.0ms	(exp (* a x))

simplify980.0ms

Calls

17 calls:

Slowest

203.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
189.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
189.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
153.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
35.0ms	(- (exp (* a x)) 1)

prune613.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

4.7b	(- (* (exp (* a x)) (exp (* a x))) (* 1 1))
0.1b	(exp (* a x))
0.1b	(exp (* a x))
0.1b	(exp (* a x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`exp-prod` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Calls

4 calls:

Slowest

18.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1 1))
2.0ms	(exp (* a x))
2.0ms	(exp (* a x))
2.0ms	(exp (* a x))

series99.0ms

Calls

4 calls:

Slowest

54.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1 1))
21.0ms	(exp (* a x))
14.0ms	(exp (* a x))
11.0ms	(exp (* a x))

simplify1.0s

Calls

21 calls:

Slowest

217.0ms	(+ (* 2 (* (pow a 2) (pow x 2))) (+ (* 2 (* a x)) (* 4/3 (* (pow a 3) (pow x 3)))))
147.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
147.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
131.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
115.0ms	(/ (exp (* (exp (* a x)) (exp (* a x)))) (exp (* 1 1)))

prune458.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes328.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch64.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2707×	body	1280	valid
385.0ms	5437×	body	80	valid
333.0ms	1298×	body	640	valid
166.0ms	744×	body	320	valid
49.0ms	417×	body	160	valid