Details

sample57.0ms

Algorithm

intervals

Results

23.0ms	66×	body	1280	valid
13.0ms	200×	body	80	valid
9.0ms	42×	body	640	valid
4.0ms	34×	body	320	valid
1.0ms	10×	body	160	valid

simplify26.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

26.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize8.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (exp x) 1)
0.0b	(/ (- (exp x) 1) x)

rewrite47.0ms

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

37.0ms	(/ (- (exp x) 1) x)
8.0ms	(- (exp x) 1)

series74.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

59.0ms	(/ (- (exp x) 1) x)
15.0ms	(- (exp x) 1)

simplify2.0s

Counts

67 → 70

Calls

67 calls:

Slowest

208.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
207.0ms	(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
136.0ms	(* -1 (/ (- 1 (exp x)) x))
70.0ms	(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
61.0ms	(- (pow (exp x) 3) (pow 1 3))

prune583.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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

18.0ms	(* x (+ (* 1/6 x) 1/2))
10.0ms	(* 1/6 x)

series127.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

109.0ms	(* x (+ (* 1/6 x) 1/2))
18.0ms	(* 1/6 x)

simplify1.0s

Counts

29 → 48

Calls

29 calls:

Slowest

257.0ms	(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
235.0ms	(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
187.0ms	(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
45.0ms	(+ (* 1/2 x) (* 1/6 (pow x 2)))
39.0ms	(+ (* 1/2 x) (* 1/6 (pow x 2)))

prune327.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

3.1b	(+ (exp (+ x (+ x x))) -1)
0.0b	(exp (+ x (+ x x)))
0.0b	(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
0.0b	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))

rewrite638.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-log-exp`
16×	`add-sqr-sqrt`
12×	`exp-prod`
11×	`distribute-lft-out`
10×	`add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
7×	`sum-log`
5×	`times-frac` `associate-/l*`
4×	`pow1` `flip3-+` `distribute-rgt1-in` `flip-+` `insert-posit16`
3×	`difference-of-sqr--1` `distribute-rgt-out` `rem-exp-log`
2×	`cbrt-undiv` `+-commutative` `distribute-lft1-in` `div-exp` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`associate-+r+` `clear-num` `associate-/r*` `frac-2neg` `exp-sum` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 82

Calls

4 calls:

Slowest

425.0ms	(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
97.0ms	(+ (exp (+ x (+ x x))) -1)
60.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
54.0ms	(exp (+ x (+ x x)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

126.0ms	(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
33.0ms	(+ (exp (+ x (+ x x))) -1)
26.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
17.0ms	(exp (+ x (+ x x)))

simplify6.8s

Counts

56 → 94

Calls

56 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))))))
712.0ms	(/ (* (* (+ (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))))))
351.0ms	(+ (pow (exp (+ x (+ x x))) 3) (pow -1 3))
349.0ms	(/ (- (exp (* 3 x)) 1) (* (+ (pow (exp x) 2) (+ (exp x) 1)) x))
340.0ms	(/ (- (exp (* 3 x)) 1) (* (+ (pow (exp x) 2) (+ (exp x) 1)) x))

prune958.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

3.1b	(+ (exp (+ x (+ x x))) -1)
3.1b	(+ (exp (+ x (+ x x))) -1)
3.1b	(+ (exp (+ x (+ x x))) -1)
0.1b	(cbrt (* (* (+ (exp (+ x (+ x x))) -1) (+ (exp (+ x (+ x x))) -1)) (+ (exp (+ x (+ x x))) -1)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`cbrt-div`
14×	`associate-*l/`
10×	`*-un-lft-identity` `add-log-exp`
8×	`associate-*r/`
7×	`add-sqr-sqrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`+-commutative` `difference-of-sqr--1` `sum-log` `distribute-lft-out`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 79

Calls

4 calls:

Slowest

862.0ms	(cbrt (* (* (+ (exp (+ x (+ x x))) -1) (+ (exp (+ x (+ x x))) -1)) (+ (exp (+ x (+ x x))) -1)))
128.0ms	(+ (exp (+ x (+ x x))) -1)
114.0ms	(+ (exp (+ x (+ x x))) -1)
100.0ms	(+ (exp (+ x (+ x x))) -1)

series128.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

36.0ms	(cbrt (* (* (+ (exp (+ x (+ x x))) -1) (+ (exp (+ x (+ x x))) -1)) (+ (exp (+ x (+ x x))) -1)))
32.0ms	(+ (exp (+ x (+ x x))) -1)
32.0ms	(+ (exp (+ x (+ x x))) -1)
27.0ms	(+ (exp (+ x (+ x x))) -1)

simplify11.4s

Counts

49 → 91

Calls

49 calls:

Slowest

1.1s	(cbrt (* (* (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))) (+ (exp (+ x (+ x x))) -1)))
678.0ms	(cbrt (* (* (+ (exp (+ x (+ x x))) -1) (+ (exp (+ x (+ x x))) -1)) (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))))
659.0ms	(cbrt (* (* (+ (exp (+ x (+ x x))) -1) (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))) (+ (exp (+ x (+ x x))) -1)))
412.0ms	(cbrt (* (* (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (+ (pow (exp (+ x (+ x x))) 3) (pow -1 3))) (+ (exp (+ x (+ x x))) -1)))
408.0ms	(cbrt (* (* (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (+ (pow (exp (+ x (+ x x))) 3) (pow -1 3))) (+ (pow (exp (+ x (+ x x))) 3) (pow -1 3))))

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.8b

bsearch80.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

870.0ms	2334×	body	1280	valid
786.0ms	1658×	body	640	valid
282.0ms	5435×	body	80	valid
132.0ms	810×	body	320	valid
62.0ms	410×	body	160	valid