Details

sample96.0ms

Algorithm

intervals

Results

66.0ms	185×	body	1280	valid
9.0ms	258×	body	80	valid
8.0ms	34×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	10×	body	160	valid

simplify70.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

70.0ms

(+ (- (exp x) 2) (exp (- x)))

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.3b

localize13.0ms

Local error

Found 2 expressions with local error:

3.8b	(+ (- (exp x) 2) (exp (- x)))
0.0b	(- (exp x) 2)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`neg-sub0` `exp-neg` `expm1-log1p-u` `pow1` `sum-log` `sub-neg` `add-cbrt-cube` `exp-diff` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+`

Counts

2 → 67

Calls

2 calls:

Slowest

45.0ms	(+ (- (exp x) 2) (exp (- x)))
15.0ms	(- (exp x) 2)

series93.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

81.0ms	(+ (- (exp x) 2) (exp (- x)))
12.0ms	(- (exp x) 2)

simplify3.4s

Counts

57 → 73

Calls

57 calls:

Slowest

442.0ms	(+ (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) (exp 0)))
343.0ms	(+ (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) 1))
275.0ms	(+ (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (exp 0)))
239.0ms	(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
177.0ms	(* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (exp x))

prune592.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) (* x x)) 1/360)
0.0b	(fma (* (* (* x x) (* x x)) 1/360) (* x x) (fma (* (* x x) (* x x)) 1/12 (* x x)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

244×	`pow1`
72×	`pow-prod-up`
59×	`pow-prod-down`
46×	`add-cbrt-cube` `add-exp-log`
44×	`pow-sqr`
36×	`pow-plus`
29×	`prod-exp` `cbrt-unprod`
26×	`pow2`
6×	`add-sqr-sqrt`
5×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`fma-udef`

Counts

4 → 174

Calls

4 calls:

Slowest

120.0ms	(* (* (* x x) (* x x)) 1/360)
44.0ms	(* (* x x) (* x x))
22.0ms	(* (* x x) (* x x))
0.0ms	(fma (* (* (* x x) (* x x)) 1/360) (* x x) (fma (* (* x x) (* x x)) 1/12 (* x x)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

83.0ms	(fma (* (* (* x x) (* x x)) 1/360) (* x x) (fma (* (* x x) (* x x)) 1/12 (* x x)))
50.0ms	(* (* (* x x) (* x x)) 1/360)
43.0ms	(* (* x x) (* x x))
42.0ms	(* (* x x) (* x x))

simplify7.9s

Counts

166 → 186

Calls

166 calls:

Slowest

542.0ms	(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 1/360 1/360) 1/360))
432.0ms	(* (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))) (* (* 1/360 1/360) 1/360))
422.0ms	(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 1/360 1/360) 1/360))
410.0ms	(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 1/360 1/360) 1/360))
385.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))

prune1.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.5b	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)
0.0b	(* (+ (exp x) 2) (exp x))
0.0b	(* (exp x) (exp x))
0.0b	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (* (+ (exp x) 2) (exp x)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`exp-prod` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube`
9×	`add-exp-log`
7×	`associate-l`
6×	`associate-r`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-*l/` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `swap-sqr` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `*-commutative` `flip-+` `unswap-sqr`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

Slowest

55.0ms	(* (+ (exp x) 2) (exp x))
14.0ms	(* (exp x) (exp x))
13.0ms	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (* (+ (exp x) 2) (exp x)))
0.0ms	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)

series321.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

196.0ms	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (* (+ (exp x) 2) (exp x)))
87.0ms	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)
22.0ms	(* (+ (exp x) 2) (exp x))
17.0ms	(* (exp x) (exp x))

simplify5.9s

Counts

77 → 110

Calls

77 calls:

Slowest

628.0ms	(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
492.0ms	(* (+ (pow (exp x) 3) (pow 2 3)) (exp x))
479.0ms	(* (- (* (exp x) (exp x)) (* 2 2)) (exp x))
361.0ms	(/ (* (* (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (fma (+ (* (exp x) (exp x)) -3) (exp x) 2)) (fma (+ (* (exp x) (exp x)) -3) (exp x) 2)) (* (* (* (+ (exp x) 2) (exp x)) (* (+ (exp x) 2) (exp x))) (* (+ (exp x) 2) (exp x))))
343.0ms	(/ (* (* (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (fma (+ (* (exp x) (exp x)) -3) (exp x) 2)) (fma (+ (* (exp x) (exp x)) -3) (exp x) 2)) (* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x))))

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

3.5b	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)
1.0b	(* (sqrt (* (+ (exp x) 2) (exp x))) (sqrt (* (+ (exp x) 2) (exp x))))
0.0b	(* (+ (exp x) 2) (exp x))
0.0b	(* (+ (exp x) 2) (exp x))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

57×	`pow1`
28×	`sqrt-pow1`
22×	`pow-prod-down`
18×	`add-sqr-sqrt` `associate-*l/`
16×	`*-un-lft-identity`
12×	`sqrt-div` `associate-l` `add-cube-cbrt`
10×	`add-cbrt-cube` `pow1/2` `associate-r` `pow-prod-up`
8×	`flip3-+` `add-exp-log` `flip-+`
6×	`pow-sqr`
4×	`expm1-log1p-u` `frac-times` `swap-sqr` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*r/` `distribute-lft-out`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `fma-udef`

Counts

4 → 119

Calls

4 calls:

Slowest

94.0ms	(* (sqrt (* (+ (exp x) 2) (exp x))) (sqrt (* (+ (exp x) 2) (exp x))))
54.0ms	(* (+ (exp x) 2) (exp x))
53.0ms	(* (+ (exp x) 2) (exp x))
1.0ms	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)

series148.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)
30.0ms	(* (+ (exp x) 2) (exp x))
28.0ms	(* (sqrt (* (+ (exp x) 2) (exp x))) (sqrt (* (+ (exp x) 2) (exp x))))
23.0ms	(* (+ (exp x) 2) (exp x))

simplify10.5s

Counts

113 → 131

Calls

113 calls:

Slowest

771.0ms	(* (* (* (sqrt (* (+ (exp x) 2) (exp x))) (sqrt (* (+ (exp x) 2) (exp x)))) (sqrt (* (+ (exp x) 2) (exp x)))) (* (* (sqrt (* (+ (exp x) 2) (exp x))) (sqrt (* (+ (exp x) 2) (exp x)))) (sqrt (* (+ (exp x) 2) (exp x)))))
681.0ms	(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
618.0ms	(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
581.0ms	(* (* (+ (exp x) 2) (exp x)) (* (+ (exp x) 2) (exp x)))
560.0ms	(* (+ (pow (exp x) 3) (pow 2 3)) (exp x))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch2.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.9s	5694×	body	1280	valid
555.0ms	7754×	body	80	valid
476.0ms	1200×	body	640	valid
177.0ms	683×	body	320	valid
36.0ms	267×	body	160	valid