Details

sample215.0ms

Algorithm

intervals

Results

98.0ms	103×	body	2560	valid
56.0ms	88×	body	1280	valid
25.0ms	263×	body	80	nan
14.0ms	30×	body	640	valid
6.0ms	17×	body	320	valid
3.0ms	14×	body	160	valid
1.0ms	4×	body	80	valid

simplify177.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

177.0ms

(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.1b	(* 5 (* v v))
0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`times-frac`
15×	`add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `difference-of-squares`
6×	`associate-/r*`
4×	`difference-of-sqr-1`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 74

Calls

3 calls:

Slowest

23.0ms	(* 5 (* v v))
21.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series116.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

81.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
31.0ms	(* 5 (* v v))
3.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify7.2s

Counts

70 → 83

Calls

70 calls:

Slowest

403.0ms	(- (* 1 1) (* (* 5 (* v v)) (* 5 (* v v))))
317.0ms	(- (pow 1 3) (pow (* 5 (* v v)) 3))
283.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
277.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
246.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))

prune704.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(acos (+ -1 (* 4 (+ (* v v) (* (* v v) (* v v))))))
0.1b	(* (* v v) (* v v))
0.0b	(* 4 (+ (* v v) (* (* v v) (* v v))))
0.0b	(+ (* v v) (* (* v v) (* v v)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
36×	`pow-prod-up`
24×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus` `add-cbrt-cube` `add-exp-log`
13×	`pow2`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`associate-r`
4×	`associate-l` `insert-posit16`
2×	`flip3-+` `distribute-rgt1-in` `associate-r/` `-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `+-commutative` `sum-log` `distribute-lft-in` `swap-sqr`

Counts

4 → 110

Calls

4 calls:

Slowest

48.0ms	(* (* v v) (* v v))
35.0ms	(* 4 (+ (* v v) (* (* v v) (* v v))))
10.0ms	(+ (* v v) (* (* v v) (* v v)))
2.0ms	(acos (+ -1 (* 4 (+ (* v v) (* (* v v) (* v v))))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(* 4 (+ (* v v) (* (* v v) (* v v))))
129.0ms	(+ (* v v) (* (* v v) (* v v)))
35.0ms	(* (* v v) (* v v))
4.0ms	(acos (+ -1 (* 4 (+ (* v v) (* (* v v) (* v v))))))

simplify5.1s

Counts

96 → 122

Calls

96 calls:

Slowest

427.0ms	(- (* v v) (* (* v v) (* v v)))
340.0ms	(* 4 (+ (* v v) (* (* v v) (* v v))))
331.0ms	(* (* (* (* v v) (* v v)) (* v v)) (* (* (* v v) v) (* (* v v) v)))
325.0ms	(* (* (* 4 4) 4) (* (* (+ (* v v) (* (* v v) (* v v))) (+ (* v v) (* (* v v) (* v v)))) (+ (* v v) (* (* v v) (* v v)))))
318.0ms	(* (* (* (* v v) v) (* (* v v) v)) (* (* (* v v) (* v v)) (* v v)))

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(acos (- (* 4 (+ (* v v) (* (* v v) (* v v)))) 1))
0.1b	(* (* v v) (* v v))
0.0b	(* 4 (+ (* v v) (* (* v v) (* v v))))
0.0b	(+ (* v v) (* (* v v) (* v v)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
36×	`pow-prod-up`
24×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus` `add-cbrt-cube` `add-exp-log`
13×	`pow2`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`associate-r`
4×	`associate-l` `insert-posit16`
2×	`flip3-+` `distribute-rgt1-in` `associate-r/` `-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `+-commutative` `sum-log` `distribute-lft-in` `swap-sqr`

Counts

4 → 110

Calls

4 calls:

Slowest

40.0ms	(* (* v v) (* v v))
28.0ms	(* 4 (+ (* v v) (* (* v v) (* v v))))
14.0ms	(+ (* v v) (* (* v v) (* v v)))
3.0ms	(acos (- (* 4 (+ (* v v) (* (* v v) (* v v)))) 1))

series277.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(* 4 (+ (* v v) (* (* v v) (* v v))))
88.0ms	(+ (* v v) (* (* v v) (* v v)))
40.0ms	(* (* v v) (* v v))
4.0ms	(acos (- (* 4 (+ (* v v) (* (* v v) (* v v)))) 1))

simplify5.2s

Counts

96 → 122

Calls

96 calls:

Slowest

445.0ms	(* (* (* (* v v) (* v v)) (* v v)) (* (* (* v v) (* v v)) (* v v)))
378.0ms	(* (* (* (* v v) (* v v)) (* v v)) (* (* (* v v) v) (* (* v v) v)))
373.0ms	(* (* (* (* v v) v) (* (* v v) v)) (* (* (* v v) (* v v)) (* v v)))
352.0ms	(- (* v v) (* (* v v) (* v v)))
335.0ms	(* (* (* 4 4) 4) (* (* (+ (* v v) (* (* v v) (* v v))) (+ (* v v) (* (* v v) (* v v)))) (+ (* v v) (* (* v v) (* v v)))))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
1.0b	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0b	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
0.2b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

Slowest

14.0ms	(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
1.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

28.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
18.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
11.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
4.0ms	(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))

simplify14.0s

Counts

82 → 99

Calls

82 calls:

Slowest

661.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
338.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
324.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
317.0ms	(sqrt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1))))
314.0ms	(sqrt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1))))

prune851.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes125.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.6s	3032×	body	2560	valid
1.7s	2478×	body	1280	valid
1.3s	8130×	body	80	nan
731.0ms	1243×	body	640	valid
253.0ms	628×	body	320	valid
126.0ms	415×	body	160	valid
27.0ms	204×	body	80	valid