Details

sample62.0ms

Algorithm

intervals

Results

23.0ms	72×	body	1280	valid
14.0ms	183×	body	80	valid
11.0ms	55×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	14×	body	160	valid

simplify29.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

29.0ms

(/ (- (exp x) 1) x)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize9.0ms

Local error

Found 2 expressions with local error:

4.4b	(- (exp x) 1)
0.0b	(/ (- (exp x) 1) x)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

Slowest

29.0ms	(/ (- (exp x) 1) x)
9.0ms	(- (exp x) 1)

series66.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

50.0ms	(/ (- (exp x) 1) x)
16.0ms	(- (exp x) 1)

simplify2.0s

Counts

67 → 70

Calls

67 calls:

Slowest

266.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
190.0ms	(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
122.0ms	(* -1 (/ (- 1 (exp x)) x))
65.0ms	(- (pow (exp x) 3) (pow 1 3))
60.0ms	(/ (- (sqrt (exp x)) (sqrt 1)) (sqrt x))

prune511.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(* 1/6 x)
0.1b	(* x (+ (* 1/6 x) 1/2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
2×	`pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 42

Calls

2 calls:

Slowest

36.0ms	(* x (+ (* 1/6 x) 1/2))
9.0ms	(* 1/6 x)

series114.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

97.0ms	(* x (+ (* 1/6 x) 1/2))
16.0ms	(* 1/6 x)

simplify996.0ms

Counts

29 → 48

Calls

29 calls:

Slowest

282.0ms	(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
193.0ms	(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
174.0ms	(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
66.0ms	(+ (* 1/2 x) (* 1/6 (pow x 2)))
56.0ms	(+ (* 1/2 x) (* 1/6 (pow x 2)))

prune348.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

4.5b	(+ (exp (+ x (+ x x))) -1)
0.0b	(* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
0.0b	(* (exp x) (exp x))
0.0b	(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))

rewrite706.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
18×	`exp-prod` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube`
11×	`add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`times-frac` `pow-prod-down` `associate-/l*`
4×	`flip3-+` `associate-*r/` `pow-sqr` `pow-prod-up` `flip-+` `insert-posit16`
3×	`difference-of-sqr--1` `swap-sqr` `prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative` `unswap-sqr` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `distribute-lft-in` `pow-plus` `div-inv`

Counts

4 → 102

Calls

4 calls:

Slowest

389.0ms	(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
162.0ms	(* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
139.0ms	(+ (exp (+ x (+ x x))) -1)
14.0ms	(* (exp x) (exp x))

series227.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
77.0ms	(* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
22.0ms	(+ (exp (+ x (+ x x))) -1)
14.0ms	(* (exp x) (exp x))

simplify9.0s

Counts

89 → 114

Calls

89 calls:

Slowest

835.0ms	(/ (* (* (+ (exp (+ x (+ x x))) -1) (+ (exp (+ x (+ x x))) -1)) (+ (exp (+ x (+ x x))) -1)) (* (* (* x x) x) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
721.0ms	(/ (* (* (+ (exp (+ x (+ x x))) -1) (+ (exp (+ x (+ x x))) -1)) (+ (exp (+ x (+ x x))) -1)) (* (* (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
398.0ms	(/ (- (exp (* 3 x)) 1) (* (+ (pow (exp x) 2) (+ (exp x) 1)) x))
394.0ms	(* (* (* x x) x) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
391.0ms	(+ (* (* (exp x) (exp x)) (* (exp x) (exp x))) (- (* (+ (* 1 1) (* (exp x) 1)) (+ (* 1 1) (* (exp x) 1))) (* (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (sqrt (exp (+ x (+ x x)))) 1)
0.0b	(* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
0.0b	(* (exp x) (exp x))
0.0b	(exp (+ x (+ x x)))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`exp-prod`
20×	`add-cube-cbrt`
13×	`pow1`
12×	`add-log-exp`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-down`
4×	`distribute-rgt1-in` `pow-sqr` `pow-prod-up` `sqrt-prod` `insert-posit16` `difference-of-squares`
3×	`sum-log` `distribute-rgt-out` `swap-sqr` `rem-exp-log`
2×	`distribute-lft1-in` `difference-of-sqr-1` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `pow-plus` `flip3--` `diff-log` `exp-sum` `flip-+` `flip--`

Counts

4 → 103

Calls

4 calls:

Slowest

168.0ms	(- (sqrt (exp (+ x (+ x x)))) 1)
138.0ms	(* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
43.0ms	(exp (+ x (+ x x)))
23.0ms	(* (exp x) (exp x))

series176.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
51.0ms	(- (sqrt (exp (+ x (+ x x)))) 1)
23.0ms	(* (exp x) (exp x))
15.0ms	(exp (+ x (+ x x)))

simplify4.9s

Counts

94 → 115

Calls

94 calls:

Slowest

408.0ms	(* (* (* x x) x) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
320.0ms	(* x (+ (pow (exp x) 2) (+ (exp x) 1)))
314.0ms	(+ (* (* (exp x) (exp x)) (* (exp x) (exp x))) (- (* (+ (* 1 1) (* (exp x) 1)) (+ (* 1 1) (* (exp x) 1))) (* (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
283.0ms	(* x (+ (pow (exp x) 2) (+ (exp x) 1)))
249.0ms	(+ (* 3/2 x) (+ (* 9/16 (pow x 3)) (* 9/8 (pow x 2))))

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.7b

bsearch79.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

969.0ms	1660×	body	640	valid
951.0ms	2267×	body	1280	valid
395.0ms	5464×	body	80	valid
167.0ms	837×	body	320	valid
155.0ms	457×	body	160	valid