Details

sample129.0ms

Algorithm

intervals

Results

59.0ms	287×	body	80	nan
49.0ms	256×	body	80	valid

simplify32.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

32.0ms

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

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

9.0ms	(/ (acos (/ (- g) h)) 3)
2.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
0.0ms	(fma 2/3 PI (/ (acos (/ (- g) h)) 3))

series194.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

133.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
48.0ms	(fma 2/3 PI (/ (acos (/ (- g) h)) 3))
12.0ms	(/ (acos (/ (- g) h)) 3)

simplify1.3s

Counts

36 → 63

Calls

36 calls:

Slowest

226.0ms	(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
94.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
90.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
88.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
72.0ms	(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))

prune713.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.0b

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
1.0b	(log1p (expm1 (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))))
1.0b	(expm1 (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3))))
1.0b	(/ (acos (/ (- g) h)) 3)

rewrite17.0ms

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`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-sub`
1×	`acos-asin` `cbrt-undiv` `acos-neg` `cos-sum` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `log1p-expm1` `distribute-frac-neg` `fma-udef` `div-inv` `expm1-udef`

Counts

4 → 67

Calls

4 calls:

Slowest

10.0ms	(/ (acos (/ (- g) h)) 3)
5.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
1.0ms	(expm1 (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3))))
0.0ms	(log1p (expm1 (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

238.0ms	(log1p (expm1 (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))))
190.0ms	(expm1 (cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3))))
141.0ms	(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
18.0ms	(/ (acos (/ (- g) h)) 3)

simplify1.6s

Counts

41 → 79

Calls

41 calls:

Slowest

239.0ms	(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
93.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
90.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
90.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
88.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.0b

localize82.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h))))
1.0b	(cos (fma 2/3 PI (* (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) 3))))
1.0b	(log1p (expm1 (cos (fma 2/3 PI (* (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) 3))))))
1.0b	(cbrt (acos (/ (- g) h)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`cbrt-prod`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
7×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `cos-sum` `log1p-udef` `pow-plus` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 80

Calls

4 calls:

Slowest

15.0ms	(* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h))))
5.0ms	(cos (fma 2/3 PI (* (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) 3))))
1.0ms	(cbrt (acos (/ (- g) h)))
0.0ms	(log1p (expm1 (cos (fma 2/3 PI (* (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) 3))))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

221.0ms	(log1p (expm1 (cos (fma 2/3 PI (* (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) 3))))))
165.0ms	(cos (fma 2/3 PI (* (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (/ (cbrt (acos (/ (- g) h))) 3))))
59.0ms	(cbrt (acos (/ (- g) h)))
55.0ms	(* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h))))

simplify3.5s

Counts

61 → 92

Calls

61 calls:

Slowest

627.0ms	(pow (acos (* -1 (/ g h))) 1/3)
378.0ms	(pow (pow (acos (* -1 (/ g h))) 2) 1/3)
358.0ms	(pow (pow (acos (* -1 (/ g h))) 2) 1/3)
333.0ms	(pow (pow (acos (* -1 (/ g h))) 2) 1/3)
251.0ms	(pow (acos (* -1 (/ g h))) 1/3)

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 1.0b

regimes203.0ms

Accuracy

0% (0.0b remaining)

Error of 1.0b against oracle of 1.0b and baseline of 1.0b

bsearch8.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	8118×	body	80	nan
1.7s	8000×	body	80	valid