Details

sample139.0ms

Algorithm

intervals

Results

89.0ms	280×	body	80	valid
19.0ms	93×	body	80	nan

simplify292.0ms

Counts: 1 → 1

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize131.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma -4 (* c a) (* b b)))
23.1b	(sqrt (fma -4 (* c a) (* b b)))
1.0b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.0b	(fma -4 (* c a) (* b b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `fma-udef` `flip--`

Counts

4 → 134

Calls

4 calls:

Slowest

11.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
3.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))
0.0ms	(fma -4 (* c a) (* b b))

series432.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

133.0ms	(sqrt (fma -4 (* c a) (* b b)))
110.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
99.0ms	(sqrt (fma -4 (* c a) (* b b)))
90.0ms	(fma -4 (* c a) (* b b))

simplify992.0ms

Counts: 146 → 146

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize161.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma -4 (* c a) (* b b)))
23.1b	(sqrt (fma -4 (* c a) (* b b)))
23.1b	(sqrt (fma -4 (* c a) (* b b)))
10.8b	(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

Slowest

15.0ms	(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
1.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
107.0ms	(sqrt (fma -4 (* c a) (* b b)))
102.0ms	(sqrt (fma -4 (* c a) (* b b)))
91.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify3.0s

Counts: 80 → 80

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

localize202.0ms

Local error

Found 4 expressions with local error:

23.8b	(cbrt (fma -4 (* c a) (* b b)))
23.8b	(cbrt (fma -4 (* c a) (* b b)))
23.8b	(cbrt (fma -4 (* c a) (* b b)))
23.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

1.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))

series923.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

306.0ms	(cbrt (fma -4 (* c a) (* b b)))
264.0ms	(cbrt (fma -4 (* c a) (* b b)))
251.0ms	(cbrt (fma -4 (* c a) (* b b)))
102.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify1.2s

Counts: 70 → 70

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.1b

localize225.0ms

Local error

Found 4 expressions with local error:

23.8b	(cbrt (fma -4 (* c a) (* b b)))
23.8b	(cbrt (fma -4 (* c a) (* b b)))
23.8b	(cbrt (fma -4 (* c a) (* b b)))
23.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

1.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))

series870.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

285.0ms	(cbrt (fma -4 (* c a) (* b b)))
252.0ms	(cbrt (fma -4 (* c a) (* b b)))
196.0ms	(cbrt (fma -4 (* c a) (* b b)))
137.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify1.1s

Counts: 70 → 70

prune1.5s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 12.1b

regimes419.0ms

Accuracy

90.7% (0.7b remaining)

Error of 13.1b against oracle of 12.4b and baseline of 19.7b

bsearch102.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.3s	8746×	body	80	valid
549.0ms	2933×	body	80	nan