Details

sample90.0ms

Algorithm

intervals

Results

37.0ms	79×	body	1280	valid
20.0ms	62×	body	640	valid
12.0ms	182×	body	80	valid
4.0ms	16×	body	320	valid
2.0ms	11×	body	160	valid

simplify81.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

81.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize17.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (exp (* a x)) 1)
0.0b	(exp (* a x))

rewrite31.0ms

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

22.0ms	(- (exp (* a x)) 1)
8.0ms	(exp (* a x))

series64.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

51.0ms	(- (exp (* a x)) 1)
13.0ms	(exp (* a x))

simplify1.3s

Counts

16 → 34

Calls

16 calls:

Slowest

244.0ms	(/ (exp (exp (* a x))) (exp 1))
144.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
142.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
132.0ms	(+ (sqrt (exp (* a x))) (sqrt 1))
130.0ms	(- (sqrt (exp (* a x))) (sqrt 1))

prune355.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

12.6b	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
2.4b	(* x (* (* a 1/6) (* (* a x) (* a x))))
0.8b	(* (* a 1/6) (* (* a x) (* a x)))
0.3b	(* a 1/6)

rewrite466.0ms

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

285.0ms	(* x (* (* a 1/6) (* (* a x) (* a x))))
97.0ms	(* (* a 1/6) (* (* a x) (* a x)))
74.0ms	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
7.0ms	(* a 1/6)

series365.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
109.0ms	(* x (* (* a 1/6) (* (* a x) (* a x))))
72.0ms	(* (* a 1/6) (* (* a x) (* a x)))
27.0ms	(* a 1/6)

simplify26.6s

Counts

91 → 132

Calls

91 calls:

Slowest

773.0ms	(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a x) (* a x)) (* (* a x) (* a x))) (* (* a x) (* a x)))))
753.0ms	(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a x) (* a x)) (* a x)))))
729.0ms	(* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a x) (* a x)) (* a x)) (* (* (* a a) a) (* (* x x) x))))
654.0ms	(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a x) (* a x)) (* a x)))))
636.0ms	(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a x) (* a x)) (* a x)) (* (* (* a a) a) (* (* x x) x)))))

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 3 expressions with local error:

2.4b	(- (exp (* a x)) 1)
2.4b	(log (exp (- (exp (* a x)) 1)))
0.0b	(exp (* a x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

Slowest

41.0ms	(log (exp (- (exp (* a x)) 1)))
29.0ms	(- (exp (* a x)) 1)
8.0ms	(exp (* a x))

series111.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

52.0ms	(- (exp (* a x)) 1)
45.0ms	(log (exp (- (exp (* a x)) 1)))
14.0ms	(exp (* a x))

simplify3.2s

Counts

33 → 60

Calls

33 calls:

Slowest

271.0ms	(log (* (cbrt (exp (- (exp (* a x)) 1))) (cbrt (exp (- (exp (* a x)) 1)))))
233.0ms	(log (sqrt (exp (- (exp (* a x)) 1))))
223.0ms	(/ (exp (exp (* a x))) (exp 1))
197.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
189.0ms	(cbrt (- (exp (* a x)) 1))

prune669.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (pow (exp (* a x)) 3) (pow 1 3))
0.0b	(pow (exp (* a x)) 3)
0.0b	(exp (* a x))
0.0b	(exp (* a x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`difference-of-squares`
21×	`unpow-prod-down` `cube-prod`
11×	`add-log-exp` `sqr-pow`
7×	`add-cube-cbrt`
6×	`distribute-lft-out--`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `insert-posit16`
3×	`pow-unpow` `exp-prod` `pow-pow` `exp-to-pow`
2×	`cube-mult` `rem-exp-log`
1×	`pow-to-exp` `difference-cubes` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `flip--` `rem-cube-cbrt`

Counts

4 → 92

Calls

4 calls:

Slowest

46.0ms	(- (pow (exp (* a x)) 3) (pow 1 3))
15.0ms	(pow (exp (* a x)) 3)
4.0ms	(exp (* a x))
4.0ms	(exp (* a x))

series144.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

73.0ms	(- (pow (exp (* a x)) 3) (pow 1 3))
43.0ms	(pow (exp (* a x)) 3)
14.0ms	(exp (* a x))
13.0ms	(exp (* a x))

simplify20.3s

Counts

92 → 104

Calls

92 calls:

Slowest

535.0ms	(- (pow (exp (* a x)) 3) 1)
503.0ms	(- (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1) 3))
494.0ms	(- (pow (sqrt (exp (* a x))) 3) (pow 1 (/ 3 2)))
489.0ms	(- (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1) 3))
485.0ms	(- (pow (sqrt (exp (* a x))) 3) (sqrt (pow 1 3)))

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes495.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch14.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	2636×	body	1280	valid
387.0ms	5567×	body	80	valid
375.0ms	1347×	body	640	valid
133.0ms	780×	body	320	valid
46.0ms	382×	body	160	valid