Details

sample56.0ms

Algorithm

intervals

Results

24.0ms	82×	body	1280	valid
9.0ms	195×	body	80	valid
8.0ms	36×	body	640	valid
3.0ms	22×	body	320	valid
2.0ms	17×	body	160	valid

simplify3.7s

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize11.0ms

Local error

Found 1 expressions with local error:

4.5b	(- (exp (* a x)) 1)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 17

Calls

1 calls:

Slowest

11.0ms

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

series51.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

51.0ms

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

simplify1.0s

Counts: 20 → 20

prune187.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

12.6b	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (* (* (* a x) (* a x)) 1/2))
0.3b	(* (* a x) (* a x))
0.3b	(* (* a x) (* a x))
0.2b	(* (* (* a x) (* a x)) 1/2)

rewrite524.0ms

Algorithm

rewrite-expression-head

Rules

100×	`pow1`
47×	`pow-prod-down`
46×	`add-cbrt-cube` `add-exp-log`
29×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-log-exp`
5×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`pow-plus` `insert-posit16`
3×	`associate-l` `*-commutative`
2×	`pow2` `swap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

Slowest

367.0ms	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (* (* (* a x) (* a x)) 1/2))
98.0ms	(* (* (* a x) (* a x)) 1/2)
32.0ms	(* (* a x) (* a x))
24.0ms	(* (* a x) (* a x))

series350.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

195.0ms	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (* (* (* a x) (* a x)) 1/2))
62.0ms	(* (* (* a x) (* a x)) 1/2)
49.0ms	(* (* a x) (* a x))
45.0ms	(* (* a x) (* a x))

simplify5.0s

Counts: 123 → 123

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

11.6b	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (log (sqrt (exp (* (* a x) (* a x))))))
5.2b	(+ (+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (log (sqrt (exp (* (* a x) (* a x)))))) (* a x))
2.7b	(log (sqrt (exp (* (* a x) (* a x)))))
0.3b	(* (* a x) (* a x))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
17×	`pow-prod-down` `add-exp-log`
16×	`add-cbrt-cube`
12×	`log-prod`
10×	`add-log-exp`
8×	`add-sqr-sqrt` `*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
6×	`associate-+r+` `sqrt-prod`
5×	`log-pow`
4×	`sum-log` `pow-sqr` `pow-prod-up` `insert-posit16`
3×	`sqrt-pow1`
2×	`+-commutative` `flip3-+` `pow-plus` `flip-+`
1×	`pow2` `associate-+l+` `exp-prod` `exp-to-pow` `pow1/2` `swap-sqr` `rem-log-exp` `associate-r` `associate-l` `*-commutative`

Counts

4 → 87

Calls

4 calls:

Slowest

2.0s	(+ (+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (log (sqrt (exp (* (* a x) (* a x)))))) (* a x))
293.0ms	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (log (sqrt (exp (* (* a x) (* a x))))))
27.0ms	(* (* a x) (* a x))
6.0ms	(log (sqrt (exp (* (* a x) (* a x)))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

252.0ms	(+ (+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (log (sqrt (exp (* (* a x) (* a x)))))) (* a x))
158.0ms	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (log (sqrt (exp (* (* a x) (* a x))))))
59.0ms	(log (sqrt (exp (* (* a x) (* a x)))))
49.0ms	(* (* a x) (* a x))

simplify3.5s

Counts: 99 → 99

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

4.4b	(+ -1 (exp (* (+ x (+ x x)) a)))
0.2b	(* (+ x (+ x x)) a)
0.0b	(* (exp (* a x)) (exp (* a x)))
0.0b	(/ (+ -1 (exp (* (+ x (+ x x)) a))) (+ 1 (+ (* (exp (* a x)) (exp (* a x))) (exp (* a x)))))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
19×	`distribute-lft-out`
18×	`add-log-exp`
16×	`times-frac`
15×	`associate-l`
13×	`pow1`
12×	`exp-prod` `exp-to-pow`
10×	`add-cbrt-cube`
8×	`add-exp-log`
6×	`associate-r` `pow-prod-down`
5×	`pow-sqr` `pow-prod-up`
4×	`associate-/r` `flip3-+` `distribute-rgt1-in` `flip-+` `insert-posit16` `associate-/l`
3×	`distribute-rgt-out` `swap-sqr`
2×	`distribute-lft1-in` `associate-l/` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `div-exp` `div-inv`

Counts

4 → 122

Calls

4 calls:

Slowest

122.0ms	(/ (+ -1 (exp (* (+ x (+ x x)) a))) (+ 1 (+ (* (exp (* a x)) (exp (* a x))) (exp (* a x)))))
47.0ms	(* (+ x (+ x x)) a)
38.0ms	(* (exp (* a x)) (exp (* a x)))
12.0ms	(+ -1 (exp (* (+ x (+ x x)) a)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

119.0ms	(/ (+ -1 (exp (* (+ x (+ x x)) a))) (+ 1 (+ (* (exp (* a x)) (exp (* a x))) (exp (* a x)))))
55.0ms	(+ -1 (exp (* (+ x (+ x x)) a)))
36.0ms	(* (+ x (+ x x)) a)
36.0ms	(* (exp (* a x)) (exp (* a x)))

simplify729.0ms

Counts: 134 → 134

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes264.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch15.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	2718×	body	1280	valid
741.0ms	1264×	body	640	valid
382.0ms	5550×	body	80	valid
130.0ms	756×	body	320	valid
78.0ms	395×	body	160	valid