Details

sample79.0ms

Algorithm

intervals

Results

45.0ms	278×	body	80	valid
15.0ms	100×	body	80	nan

simplify327.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize155.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma -4 (* c a) (* b b)))
21.9b	(sqrt (fma -4 (* c a) (* b b)))
0.9b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
0.6b	(fma -4 (* c a) (* b b))

rewrite20.0ms

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)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
0.0ms	(fma -4 (* c a) (* b b))

series489.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(sqrt (fma -4 (* c a) (* b b)))
132.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
124.0ms	(sqrt (fma -4 (* c a) (* b b)))
96.0ms	(fma -4 (* c a) (* b b))

simplify485.0ms

Counts: 212 → 146

prune2.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.0b

localize151.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma -4 (* c a) (* b b)))
21.9b	(sqrt (fma -4 (* c a) (* b b)))
21.9b	(sqrt (fma -4 (* c a) (* b b)))
8.8b	(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)

rewrite35.0ms

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

28.0ms	(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series882.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

557.0ms	(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
111.0ms	(sqrt (fma -4 (* c a) (* b b)))
108.0ms	(sqrt (fma -4 (* c a) (* b b)))
106.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify836.0ms

Counts: 89 → 80

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize206.0ms

Local error

Found 4 expressions with local error:

22.6b	(cbrt (fma -4 (* c a) (* b b)))
22.6b	(cbrt (fma -4 (* c a) (* b b)))
22.6b	(cbrt (fma -4 (* c a) (* b b)))
21.9b	(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)))

series890.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

284.0ms	(cbrt (fma -4 (* c a) (* b b)))
257.0ms	(cbrt (fma -4 (* c a) (* b b)))
232.0ms	(cbrt (fma -4 (* c a) (* b b)))
117.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify832.0ms

Counts: 77 → 70

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize218.0ms

Local error

Found 4 expressions with local error:

22.6b	(cbrt (fma -4 (* c a) (* b b)))
22.6b	(cbrt (fma -4 (* c a) (* b b)))
21.9b	(sqrt (fma -4 (* c a) (* b b)))
21.9b	(sqrt (fma -4 (* c a) (* b b)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

Slowest

3.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(cbrt (fma -4 (* c a) (* b b)))
2.0ms	(cbrt (fma -4 (* c a) (* b b)))

series698.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

258.0ms	(cbrt (fma -4 (* c a) (* b b)))
216.0ms	(cbrt (fma -4 (* c a) (* b b)))
129.0ms	(sqrt (fma -4 (* c a) (* b b)))
95.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify939.0ms

Counts: 78 → 72

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.0b

regimes351.0ms

Accuracy

90.7% (0.7b remaining)

Error of 12.8b against oracle of 12.2b and baseline of 19.2b

bsearch87.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.4s	8715×	body	80	valid
532.0ms	2926×	body	80	nan