Details

sample97.0ms

Algorithm

intervals

Results

50.0ms	95×	body	1280	valid
13.0ms	41×	body	640	valid
11.0ms	159×	body	80	valid
6.0ms	28×	body	320	valid
1.0ms	9×	body	160	valid

simplify58.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

57.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize16.0ms

Local error

Found 2 expressions with local error:

3.1b	(- (exp (* a x)) 1)
0.0b	(exp (* a x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

2 → 28

Calls

2 calls:

Slowest

19.0ms	(- (exp (* a x)) 1)
8.0ms	(exp (* a x))

series55.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

37.0ms	(- (exp (* a x)) 1)
18.0ms	(exp (* a x))

simplify1.3s

Counts

16 → 34

Calls

16 calls:

Slowest

215.0ms	(/ (exp (exp (* a x))) (exp 1))
143.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
136.0ms	(- (sqrt (exp (* a x))) (sqrt 1))
133.0ms	(+ (sqrt (exp (* a x))) (sqrt 1))
125.0ms	(+ (sqrt (exp (* a x))) 1)

prune347.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

13.6b	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
3.0b	(* x (* (* a 1/6) (* (* a x) (* a x))))
1.0b	(* (* a 1/6) (* (* a x) (* a x)))
0.3b	(* a 1/6)

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

100×	`pow1` `add-cbrt-cube` `add-exp-log`
74×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

Slowest

254.0ms	(* x (* (* a 1/6) (* (* a x) (* a x))))
124.0ms	(* (* a 1/6) (* (* a x) (* a x)))
48.0ms	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
10.0ms	(* a 1/6)

series307.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
105.0ms	(* x (* (* a 1/6) (* (* a x) (* a x))))
48.0ms	(* (* a 1/6) (* (* a x) (* a x)))
17.0ms	(* a 1/6)

simplify26.9s

Counts

91 → 132

Calls

91 calls:

Slowest

1.2s	(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a x) (* a x)) (* a x)) (* (* (* a a) a) (* (* x x) x)))))
748.0ms	(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a a) a) (* (* x x) x)))))
665.0ms	(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a x) (* a x)) (* a x)))))
653.0ms	(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a x) (* a x)) (* (* a x) (* a x))) (* (* a x) (* a x)))))
647.0ms	(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a a) a) (* (* x x) x)))))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

3.1b	(- (exp (* a x)) 1)
0.0b	(exp (* a x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

2 → 28

Calls

2 calls:

Slowest

14.0ms	(- (exp (* a x)) 1)
4.0ms	(exp (* a x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

37.0ms	(- (exp (* a x)) 1)
26.0ms	(exp (* a x))

simplify1.2s

Counts

16 → 34

Calls

16 calls:

Slowest

179.0ms	(/ (exp (exp (* a x))) (exp 1))
157.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
150.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
127.0ms	(- (sqrt (exp (* a x))) (sqrt 1))
110.0ms	(+ (sqrt (exp (* a x))) (sqrt 1))

prune240.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (sqrt (exp (* a x))) 1)
0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.0b	(sqrt (exp (* a x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
7×	`sqrt-prod`
5×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `difference-of-squares`
3×	`exp-prod` `sqrt-pow1` `exp-to-pow`
2×	`difference-of-sqr-1` `distribute-lft-out--` `rem-exp-log`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `pow1/2` `diff-log` `flip--`

Counts

4 → 59

Calls

4 calls:

Slowest

28.0ms	(- (sqrt (exp (* a x))) 1)
8.0ms	(exp (* a x))
8.0ms	(exp (* a x))
5.0ms	(sqrt (exp (* a x)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(- (sqrt (exp (* a x))) 1)
22.0ms	(sqrt (exp (* a x)))
22.0ms	(exp (* a x))
14.0ms	(exp (* a x))

simplify2.7s

Counts

39 → 71

Calls

39 calls:

Slowest

214.0ms	(+ (* 1/2 (* a x)) (+ (* 1/8 (* (pow a 2) (pow x 2))) 1))
177.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
167.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
147.0ms	(+ (sqrt (sqrt (exp (* a x)))) 1)
144.0ms	(+ (* 1/8 (* (pow a 2) (pow x 2))) (+ (* 1/2 (* a x)) (* 1/48 (* (pow a 3) (pow x 3)))))

prune712.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes381.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.0b

bsearch6.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2760×	body	1280	valid
784.0ms	5466×	body	80	valid
373.0ms	1292×	body	640	valid
142.0ms	786×	body	320	valid
73.0ms	375×	body	160	valid