Details

sample254.0ms

Algorithm

intervals

Results

93.0ms	93×	body	2560	valid
57.0ms	77×	body	1280	valid
29.0ms	251×	body	80	nan
26.0ms	48×	body	640	valid
8.0ms	18×	body	320	valid
4.0ms	14×	body	160	valid
1.0ms	6×	body	80	valid

simplify159.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

159.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize29.0ms

Local error

Found 3 expressions with local error:

0.7b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.1b	(* 5 (* v v))
0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))

rewrite43.0ms

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

27.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
13.0ms	(* 5 (* v v))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series117.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

71.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
42.0ms	(* 5 (* v v))
4.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify7.4s

Counts

70 → 83

Calls

70 calls:

Slowest

449.0ms	(- (* 1 1) (* (* 5 (* v v)) (* 5 (* v v))))
429.0ms	(- (pow 1 3) (pow (* 5 (* v v)) 3))
288.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
279.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
264.0ms	(/ (- 1 (* 5 (* v v))) (sqrt (- (* v v) 1)))

prune624.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.1b	(* 5 (* v v))
0.0b	(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

Slowest

34.0ms	(* 5 (* v v))
19.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
14.0ms	(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
2.0ms	(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
45.0ms	(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
28.0ms	(* 5 (* v v))
4.0ms	(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify9.9s

Counts

80 → 103

Calls

80 calls:

Slowest

414.0ms	(- (* 1 1) (* (* 5 (* v v)) (* 5 (* v v))))
400.0ms	(- (pow 1 3) (pow (* 5 (* v v)) 3))
333.0ms	(- (* 1/2 PI) (asin (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1))))
325.0ms	(asin (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
324.0ms	(- (* 1/2 PI) (asin (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1))))

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.1b	(* 5 (* v v))
0.0b	(exp (log (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
0.0b	(log (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-exp-log`
9×	`add-sqr-sqrt` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`log-prod`
4×	`exp-prod` `insert-posit16` `add-log-exp`
3×	`associate-l` `exp-sum` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`log-pow`
1×	`acos-asin` `rem-log-exp` `associate-r` `*-commutative` `unswap-sqr` `rem-exp-log`

Counts

4 → 58

Calls

4 calls:

Slowest

13.0ms	(* 5 (* v v))
7.0ms	(exp (log (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
1.0ms	(log (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

83.0ms	(log (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
28.0ms	(* 5 (* v v))
4.0ms	(exp (log (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
3.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify4.9s

Counts

34 → 70

Calls

34 calls:

Slowest

389.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
352.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
337.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
331.0ms	(log (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1))))
324.0ms	(log (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1))))

prune681.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.7b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.7b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.1b	(* 5 (* v v))
0.1b	(* 5 (* v v))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
2×	`acos-asin` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

Slowest

24.0ms	(* 5 (* v v))
13.0ms	(* 5 (* v v))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

44.0ms	(* 5 (* v v))
35.0ms	(* 5 (* v v))
6.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
6.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify2.9s

Counts

32 → 70

Calls

32 calls:

Slowest

310.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
293.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
291.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
281.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
267.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

regimes234.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch4.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.7s	2948×	body	2560	valid
1.9s	2503×	body	1280	valid
834.0ms	8062×	body	80	nan
809.0ms	1276×	body	640	valid
268.0ms	643×	body	320	valid
134.0ms	428×	body	160	valid
26.0ms	202×	body	80	valid