Details

sample139.0ms

Algorithm

intervals

Results

59.0ms	256×	body	80	valid
56.0ms	264×	body	80	nan

simplify61.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

61.0ms

(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize40.0ms

Local error

Found 3 expressions with local error:

1.0b	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
0.9b	(/ (acos (/ (- g) h)) 3)
0.0b	(fma 2/3 PI (/ (acos (/ (- g) h)) 3))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`div-sub` `fma-udef`
1×	`acos-asin` `cbrt-undiv` `acos-neg` `cos-sum` `clear-num` `frac-2neg` `div-exp` `distribute-frac-neg` `div-inv`

Counts

3 → 54

Calls

3 calls:

Slowest

10.0ms	(/ (acos (/ (- g) h)) 3)
5.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
0.0ms	(fma 2/3 PI (/ (acos (/ (- g) h)) 3))

series207.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

151.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
35.0ms	(fma 2/3 PI (/ (acos (/ (- g) h)) 3))
20.0ms	(/ (acos (/ (- g) h)) 3)

simplify1.4s

Counts

36 → 63

Calls

36 calls:

Slowest

230.0ms	(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
90.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
82.0ms	(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
79.0ms	(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
62.0ms	(* 1/3 (acos (* -1 (/ g h))))

prune766.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
0.9b	(/ (acos (/ (- g) h)) 3)
0.0b	(fma 2/3 PI (/ (acos (/ (- g) h)) 3))
0.0b	(log (exp (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod` `associate-/r` `fma-udef` `associate-/l`
2×	`cos-sum` `div-sub`
1×	`acos-asin` `cbrt-undiv` `acos-neg` `log-div` `clear-num` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `distribute-frac-neg` `div-inv`

Counts

4 → 73

Calls

4 calls:

Slowest

10.0ms	(/ (acos (/ (- g) h)) 3)
8.0ms	(log (exp (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))))
5.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
1.0ms	(fma 2/3 PI (/ (acos (/ (- g) h)) 3))

series338.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(log (exp (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))))
126.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
51.0ms	(fma 2/3 PI (/ (acos (/ (- g) h)) 3))
25.0ms	(/ (acos (/ (- g) h)) 3)

simplify2.0s

Counts

47 → 85

Calls

47 calls:

Slowest

244.0ms	(log (exp (* (cos (* 2/3 PI)) (cos (/ (acos (/ (- g) h)) 3)))))
220.0ms	(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
95.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
94.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
93.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune952.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

1.0b	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
1.0b	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
1.0b	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
0.9b	(/ (acos (/ (- g) h)) 3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-sum` `associate-/r` `fma-udef` `associate-/l`
2×	`div-sub`
1×	`acos-asin` `cbrt-undiv` `acos-neg` `clear-num` `frac-2neg` `div-exp` `distribute-frac-neg` `div-inv`

Counts

4 → 65

Calls

4 calls:

Slowest

10.0ms	(/ (acos (/ (- g) h)) 3)
5.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
5.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
4.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
140.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
118.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
15.0ms	(/ (acos (/ (- g) h)) 3)

simplify1.4s

Counts

41 → 77

Calls

41 calls:

Slowest

207.0ms	(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
90.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
71.0ms	(/ (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (* (cbrt 3) (cbrt 3)))
64.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
63.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune1.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(cos (fma 2/3 PI (* (* (/ (cbrt (acos (/ (- g) h))) (sqrt 3)) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) (sqrt 3)))))
1.0b	(cbrt (acos (/ (- g) h)))
1.0b	(cbrt (acos (/ (- g) h)))
1.0b	(cbrt (acos (/ (- g) h)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 53

Calls

4 calls:

Slowest

2.0ms	(cos (fma 2/3 PI (* (* (/ (cbrt (acos (/ (- g) h))) (sqrt 3)) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) (sqrt 3)))))
1.0ms	(cbrt (acos (/ (- g) h)))
1.0ms	(cbrt (acos (/ (- g) h)))
1.0ms	(cbrt (acos (/ (- g) h)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

286.0ms	(cos (fma 2/3 PI (* (* (/ (cbrt (acos (/ (- g) h))) (sqrt 3)) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) (sqrt 3)))))
68.0ms	(cbrt (acos (/ (- g) h)))
68.0ms	(cbrt (acos (/ (- g) h)))
51.0ms	(cbrt (acos (/ (- g) h)))

simplify2.8s

Counts

22 → 65

Calls

22 calls:

Slowest

272.0ms	(pow (acos (* -1 (/ g h))) 1/3)
249.0ms	(pow (acos (* -1 (/ g h))) 1/3)
247.0ms	(pow (acos (* -1 (/ g h))) 1/3)
247.0ms	(pow (acos (* -1 (/ g h))) 1/3)
228.0ms	(pow (acos (* -1 (/ g h))) 1/3)

prune974.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes368.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch4.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
1.6s	7956×	body	80	nan