Details

sample136.0ms

Algorithm

intervals

Results

36.0ms	268×	body	80	nan
30.0ms	151×	body	160	valid
26.0ms	524×	pre	80	true
14.0ms	47×	body	320	valid
6.0ms	58×	body	80	valid

simplify462.0ms

Counts: 1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.2b

localize50.0ms

Local error

Found 4 expressions with local error:

39.7b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.3b	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
0.1b	(fma c (* -3 a) (* b b))
0.1b	(sqrt (fma c (* -3 a) (* b b)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `fma-neg` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

Slowest

19.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
15.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -3 a) (* b b)))
0.0ms	(fma c (* -3 a) (* b b))

series415.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
110.0ms	(sqrt (fma c (* -3 a) (* b b)))
88.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
80.0ms	(fma c (* -3 a) (* b b))

simplify1.5s

Counts: 114 → 114

prune1.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 41.5b

localize30.0ms

Local error

Found 4 expressions with local error:

44.7b	(fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))
0.3b	(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
0.1b	(fma c (* -3 a) (* b b))
0.1b	(fma c (* -3 a) (* b b))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

Slowest

9.0ms	(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
0.0ms	(fma c (* -3 a) (* b b))
0.0ms	(fma c (* -3 a) (* b b))
0.0ms	(fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

676.0ms	(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
396.0ms	(fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))
64.0ms	(fma c (* -3 a) (* b b))
60.0ms	(fma c (* -3 a) (* b b))

simplify1.3s

Counts: 69 → 69

prune1.1s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 41.4b

localize97.0ms

Local error

Found 4 expressions with local error:

44.7b	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))
0.6b	(cbrt (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))))
0.5b	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))
0.3b	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r`
5×	`fma-udef`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 87

Calls

4 calls:

Slowest

28.0ms	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))
10.0ms	(cbrt (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))))
6.0ms	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))
0.0ms	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))

series770.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

411.0ms	(fma (sqrt (sqrt (cbrt (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))
175.0ms	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))
113.0ms	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))
71.0ms	(cbrt (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))))

simplify1.8s

Counts: 99 → 99

prune1.8s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 41.4b

localize46.0ms

Local error

Found 4 expressions with local error:

44.7b	(fma (sqrt (sqrt (pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))
3.6b	(pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3)
0.5b	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))
0.3b	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
17×	`add-exp-log`
13×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
12×	`pow-pow`
11×	`add-cbrt-cube`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-prod-down` `prod-exp`
6×	`associate-r`
5×	`pow2` `pow-sqr` `fma-udef`
4×	`expm1-log1p-u` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `pow-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `unpow-prod-down` `unpow1/3` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

Slowest

24.0ms	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))
19.0ms	(pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3)
6.0ms	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))
0.0ms	(fma (sqrt (sqrt (pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))

series926.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

417.0ms	(fma (sqrt (sqrt (pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))
219.0ms	(pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3)
200.0ms	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))
91.0ms	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))

simplify2.4s

Counts: 118 → 118

prune2.2s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 41.4b

regimes999.0ms

Accuracy

0% (2.7b remaining)

Error of 42.6b against oracle of 39.9b and baseline of 42.6b

bsearch5.0ms

end0.0ms

sample5.8s

Algorithm

intervals

Results

1.7s	4806×	body	160	valid
1.5s	8189×	body	80	nan
1.1s	16189×	pre	80	true
605.0ms	1372×	body	320	valid
227.0ms	1822×	body	80	valid