Details

sample98.0ms

Algorithm

intervals

Results

77.0ms

431×

body

valid

simplify405.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

405.0ms

(fabs (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize120.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
0.1b	(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b	(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b	(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))

rewrite10.4s

Algorithm

rewrite-expression-head

Rules

181×	`add-exp-log`
128×	`prod-exp`
107×	`add-cbrt-cube`
70×	`cbrt-unprod`
51×	`pow1`
48×	`associate-l`
46×	`add-sqr-sqrt`
40×	`times-frac`
35×	`*-un-lft-identity` `pow-prod-down`
33×	`add-cube-cbrt`
19×	`div-exp`
15×	`associate-*l/`
14×	`sqrt-prod`
12×	`frac-add`
11×	`cbrt-undiv`
8×	`rec-exp` `1-exp`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`associate-r` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative` `div-inv`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 187

Calls

4 calls:

Slowest

8.6s	(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.7s	(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
91.0ms	(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms	(sqrt PI)

series575.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

421.0ms	(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
100.0ms	(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
53.0ms	(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify1.1m

Counts

208 → 197

Calls

208 calls:

Slowest

1.5s	(* (/ 1 (sqrt PI)) (+ (pow (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) 3) (pow (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) 3)))
1.5s	(* (* (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))) (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
1.2s	(* (/ 1 (sqrt PI)) (- (* (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) (* (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
1.2s	(* 1 (- (* (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) (* (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
972.0ms	(* 1 (+ (pow (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) 3) (pow (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) 3)))

prune3.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt PI) (cbrt PI))
1.0b	(sqrt (* (cbrt PI) (cbrt PI)))
1.0b	(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
1.0b	(cbrt PI)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`pow1`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`cbrt-prod` `pow1/3`
18×	`sqrt-pow1`
12×	`times-frac`
11×	`pow-flip`
10×	`add-exp-log`
6×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `pow-prod-down` `pow-sqr` `pow-prod-up`
5×	`sqrt-prod`
4×	`associate-/r*` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow2` `pow-plus` `associate-/l*`
2×	`pow1/2` `div-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow`

Counts

4 → 119

Calls

4 calls:

Slowest

16.0ms	(sqrt (* (cbrt PI) (cbrt PI)))
15.0ms	(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
14.0ms	(* (cbrt PI) (cbrt PI))
1.0ms	(cbrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(* (cbrt PI) (cbrt PI))
0.0ms	(sqrt (* (cbrt PI) (cbrt PI)))
0.0ms	(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
0.0ms	(cbrt PI)

simplify2.8s

Counts

144 → 123

Calls

144 calls:

Slowest

247.0ms	(fabs (* (/ 1 (sqrt (* (cbrt PI) (cbrt PI)))) (/ (+ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5)) (* (+ 2 (* 2/3 (* (fabs x) (fabs x)))) (fabs x))) (sqrt (cbrt PI)))))
223.0ms	(fabs (* (/ 1 (sqrt (* (cbrt PI) (cbrt PI)))) (/ (+ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5)) (* (+ 2 (* 2/3 (* (fabs x) (fabs x)))) (fabs x))) (sqrt (cbrt PI)))))
205.0ms	(/ (* (* 1 1) 1) (* (* (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (* (cbrt PI) (cbrt PI)))) (sqrt (* (cbrt PI) (cbrt PI)))))
205.0ms	(fabs (* (/ 1 (sqrt (* (cbrt PI) (cbrt PI)))) (/ (+ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5)) (* (+ 2 (* 2/3 (* (fabs x) (fabs x)))) (fabs x))) (sqrt (cbrt PI)))))
196.0ms	(fabs (* (/ 1 (sqrt (* (cbrt PI) (cbrt PI)))) (/ (+ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5)) (* (+ 2 (* 2/3 (* (fabs x) (fabs x)))) (fabs x))) (sqrt (cbrt PI)))))

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
0.3b	(/ (fabs x) (sqrt PI))
0.2b	(* (* (fabs x) (fabs x)) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `flip3-+` `div-exp` `associate-l` `*-commutative` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

Slowest

103.0ms	(* (* (fabs x) (fabs x)) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3))
4.0ms	(/ (fabs x) (sqrt PI))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series201.0ms

Counts

4 → 8

Calls

4 calls:

Slowest

105.0ms	(/ (fabs x) (sqrt PI))
95.0ms	(* (* (fabs x) (fabs x)) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify5.1s

Counts

123 → 100

Calls

123 calls:

Slowest

423.0ms	(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (+ (* (* (fabs x) (fabs x)) 1/5) 2/3) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3)) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3)))
358.0ms	(* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (+ (* (* (fabs x) (fabs x)) 1/5) 2/3) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3)) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3)))
282.0ms	(* (* (* (* (fabs x) (fabs x)) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3)) (* (* (fabs x) (fabs x)) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3))) (* (* (fabs x) (fabs x)) (+ (* (* (fabs x) (fabs x)) 1/5) 2/3)))
243.0ms	(* (* (fabs x) (fabs x)) (- (* (* (* (fabs x) (fabs x)) 1/5) (* (* (fabs x) (fabs x)) 1/5)) (* 2/3 2/3)))
230.0ms	(* (pow (fabs x) 2) (+ 2/3 (* 1/5 (pow (fabs x) 2))))

prune1.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
0.3b	(/ (fabs x) (sqrt PI))
0.3b	(/ (fabs x) (sqrt PI))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
30×	`sqrt-prod`
12×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/l*`
4×	`insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 108

Calls

4 calls:

Slowest

4.0ms	(/ (fabs x) (sqrt PI))
4.0ms	(/ (fabs x) (sqrt PI))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series175.0ms

Counts

4 → 8

Calls

4 calls:

Slowest

111.0ms	(/ (fabs x) (sqrt PI))
64.0ms	(/ (fabs x) (sqrt PI))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify2.6s

Counts

156 → 116

Calls

156 calls:

Slowest

281.0ms	(/ (* (* (fabs x) (fabs x)) (fabs x)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
214.0ms	(fabs (+ (* (/ (/ (fabs x) (sqrt PI)) (/ 21 (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (fabs x) (fabs x)) (fabs x))) (* (/ (fabs x) (sqrt PI)) (+ 2 (* (+ (* 1/5 (* (fabs x) (fabs x))) 2/3) (* (fabs x) (fabs x)))))))
212.0ms	(* (* (/ (fabs x) (sqrt PI)) (/ (fabs x) (sqrt PI))) (/ (fabs x) (sqrt PI)))
191.0ms	(/ (* (* (fabs x) (fabs x)) (fabs x)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
169.0ms	(* (* (/ (fabs x) (sqrt PI)) (/ (fabs x) (sqrt PI))) (/ (fabs x) (sqrt PI)))

prune1.6s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes346.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch9.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

4.6s

14000×

body

valid