Details

sample1.5s

Algorithm

intervals

Results

1.5s

3253×

body

valid

simplify830.0ms

Calls

1 calls:

Slowest

829.0ms

(* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))))

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
0.5b	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.5b	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.4b	(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

969×	`add-exp-log`
723×	`times-frac`
576×	`div-exp`
497×	`add-sqr-sqrt`
361×	`*-un-lft-identity`
328×	`add-cube-cbrt`
305×	`prod-exp`
247×	`add-cbrt-cube`
144×	`pow1`
129×	`associate-l`
120×	`cbrt-undiv`
98×	`swap-sqr`
96×	`rec-exp` `1-exp`
87×	`associate-r`
75×	`cbrt-unprod`
74×	`pow-div`
69×	`div-inv`
55×	`unswap-sqr`
37×	`pow-flip` `inv-pow`
35×	`pow-prod-up`
13×	`pow-prod-down`
11×	`pow-sqr`
7×	`frac-times` `associate-*r/`
5×	`associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `pow-plus` `*-commutative` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `cube-unmult`

Calls

4 calls:

Slowest

57.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
37.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
27.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series184.0ms

Calls

4 calls:

Slowest

76.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
56.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
52.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify2.0m

Calls

861 calls:

Slowest

931.0ms	(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))))
925.0ms	(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
845.0ms	(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))))
844.0ms	(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
825.0ms	(* (/ (/ (sqrt 1) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x)))))

prune12.2s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.3b

localize70.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
0.5b	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.3b	(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))
0.3b	(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

464×	`times-frac`
305×	`add-sqr-sqrt`
240×	`*-un-lft-identity`
224×	`add-cube-cbrt`
108×	`add-exp-log`
63×	`div-exp`
49×	`swap-sqr`
45×	`add-cbrt-cube`
43×	`associate-r` `associate-l`
39×	`sqrt-prod`
37×	`div-inv`
36×	`pow1`
25×	`prod-exp` `unswap-sqr`
22×	`associate-/r*`
21×	`cbrt-undiv`
16×	`pow-div`
10×	`rec-exp` `1-exp`
9×	`cbrt-unprod`
8×	`pow-flip` `inv-pow`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr` `associate-/l*`
1×	`pow2` `frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `associate-l/` `associate-r/` `associate-/r/` `*-commutative` `fma-udef`

Calls

4 calls:

Slowest

46.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
18.0ms	(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
2.0ms	(sqrt PI)
0.0ms	(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))

series789.0ms

Calls

4 calls:

Slowest

472.0ms	(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
276.0ms	(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))
41.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify1.4m

Calls

468 calls:

Slowest

1.3s	(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
877.0ms	(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))))
799.0ms	(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
772.0ms	(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))))
747.0ms	(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))

prune6.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 3/4 (pow (fabs x) 5))
0.3b	(/ 15/8 (pow (fabs x) 7))
0.3b	(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
0.3b	(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt` `times-frac`
48×	`*-un-lft-identity`
47×	`add-cube-cbrt`
25×	`add-exp-log`
24×	`unpow-prod-down`
19×	`add-cbrt-cube`
16×	`associate-l` `sqrt-prod`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`pow-to-exp` `pow-exp` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `pow-prod-down` `associate-l/` `-commutative`

Calls

4 calls:

Slowest

33.0ms	(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
21.0ms	(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
10.0ms	(/ 3/4 (pow (fabs x) 5))
10.0ms	(/ 15/8 (pow (fabs x) 7))

series744.0ms

Calls

4 calls:

Slowest

573.0ms	(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
82.0ms	(/ 15/8 (pow (fabs x) 7))
53.0ms	(/ 3/4 (pow (fabs x) 5))
36.0ms	(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify18.3s

Calls

169 calls:

Slowest

493.0ms	(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
377.0ms	(/ (* (* 15/8 15/8) 15/8) (* (* (pow (fabs x) 7) (pow (fabs x) 7)) (pow (fabs x) 7)))
366.0ms	(* (sqrt (sqrt (/ 1 PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
365.0ms	(/ (* (* 3/4 3/4) 3/4) (* (* (pow (fabs x) 5) (pow (fabs x) 5)) (pow (fabs x) 5)))
359.0ms	(* (sqrt 1) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))

prune3.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
0.5b	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.3b	(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

326×	`times-frac`
232×	`add-sqr-sqrt`
166×	`*-un-lft-identity`
150×	`add-cube-cbrt`
104×	`add-exp-log`
60×	`div-exp`
49×	`swap-sqr`
43×	`associate-r` `associate-l`
40×	`add-cbrt-cube`
37×	`pow1`
32×	`div-inv`
25×	`prod-exp` `unswap-sqr`
18×	`cbrt-undiv`
16×	`pow-div`
10×	`rec-exp` `1-exp`
9×	`cbrt-unprod`
8×	`pow-flip` `inv-pow`
6×	`sqrt-prod`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Calls

4 calls:

Slowest

39.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
0.0ms	(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))

series337.0ms

Calls

4 calls:

Slowest

283.0ms	(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))
53.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify33.3s

Calls

309 calls:

Slowest

888.0ms	(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
863.0ms	(* (/ (/ (sqrt 1) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
856.0ms	(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))))
768.0ms	(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))))
754.0ms	(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))

prune5.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes301.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch8.0ms

end0.0ms

sample43.6s

Algorithm

intervals

Results

42.1s

107501×

body

valid