Details

sample170.0ms

Algorithm

intervals

Results

36.0ms	16×	body	640	valid
34.0ms	109×	body	320	valid
26.0ms	491×	pre	80	true
23.0ms	235×	body	80	nan
23.0ms	105×	body	160	valid
2.0ms	26×	body	80	valid

simplify135.0ms

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize19.0ms

Local error

Found 4 expressions with local error:

29.6b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.2b	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
0.1b	(fma c (* -3 a) (* b b))
0.0b	(sqrt (fma c (* -3 a) (* b b)))

rewrite58.0ms

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

38.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
16.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -3 a) (* b b)))
0.0ms	(fma c (* -3 a) (* b b))

series393.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
122.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
81.0ms	(sqrt (fma c (* -3 a) (* b b)))
67.0ms	(fma c (* -3 a) (* b b))

simplify1.5s

Counts: 114 → 114

prune1.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 49.3b

localize31.0ms

Local error

Found 4 expressions with local error:

51.9b	(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))

rewrite8.0ms

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

7.0ms	(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
0.0ms	(fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))
0.0ms	(fma c (* -3 a) (* b b))
0.0ms	(fma c (* -3 a) (* b b))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

632.0ms	(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
439.0ms	(fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b))
87.0ms	(fma c (* -3 a) (* b b))
63.0ms	(fma c (* -3 a) (* b b))

simplify1.3s

Counts: 69 → 69

prune1.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 49.3b

localize71.0ms

Local error

Found 4 expressions with local error:

51.9b	(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))))
0.4b	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))
0.4b	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))

rewrite50.0ms

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

26.0ms	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))
16.0ms	(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))

series756.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

380.0ms	(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))
185.0ms	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))
96.0ms	(cbrt (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))))
96.0ms	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))

simplify1.8s

Counts: 99 → 99

prune1.9s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 49.2b

localize69.0ms

Local error

Found 4 expressions with local error:

51.5b	(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))
4.4b	(pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3)
0.4b	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))
0.4b	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))

rewrite50.0ms

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

20.0ms	(pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3)
16.0ms	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))
11.0ms	(* (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))

series933.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

426.0ms	(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))
245.0ms	(pow (* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b))) 1/3)
181.0ms	(* (* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b))) (fma c (* -3 a) (* b b)))
81.0ms	(* (fma c (* -3 a) (* b b)) (fma c (* -3 a) (* b b)))

simplify2.0s

Counts: 118 → 118

prune2.0s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 49.2b

regimes929.0ms

Accuracy

0% (2.0b remaining)

Error of 51.3b against oracle of 49.3b and baseline of 51.3b

bsearch9.0ms

end0.0ms

sample6.2s

Algorithm

intervals

Results

1.5s	16027×	pre	80	true
1.5s	3653×	body	320	valid
1.2s	2927×	body	160	valid
1.1s	8027×	body	80	nan
308.0ms	525×	body	640	valid
126.0ms	895×	body	80	valid