Details

sample64.0ms

Algorithm

intervals

Results

35.0ms	274×	body	80	valid
9.0ms	80×	body	80	nan

simplify302.0ms

Counts: 1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize136.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b b) (* (* 4 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4 a) c)))
1.0b	(- (* b b) (* (* 4 a) c))
1.0b	(- (* b b) (* (* 4 a) c))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

Slowest

23.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms	(- (* b b) (* (* 4 a) c))
16.0ms	(- (* b b) (* (* 4 a) c))

series345.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
77.0ms	(- (* b b) (* (* 4 a) c))
63.0ms	(- (* b b) (* (* 4 a) c))

simplify725.0ms

Counts: 82 → 82

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize178.0ms

Local error

Found 4 expressions with local error:

52.8b	(fma (- c) (* 4 a) (* c (* 4 a)))
21.4b	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))
21.4b	(sqrt (- (* b b) (* (* 4 a) c)))
1.3b	(fma b b (- (* c (* 4 a))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`
1×	`flip3-+` `flip3--` `flip-+` `hypot-def` `flip--` `distribute-lft-out`

Counts

4 → 60

Calls

4 calls:

Slowest

19.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))
1.0ms	(fma (- c) (* 4 a) (* c (* 4 a)))
0.0ms	(fma b b (- (* c (* 4 a))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))
113.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
90.0ms	(fma b b (- (* c (* 4 a))))
51.0ms	(fma (- c) (* 4 a) (* c (* 4 a)))

simplify1.7s

Counts: 72 → 72

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize178.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b b) (* (* 4 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4 a) c)))
11.4b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`fma-def` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `neg-mul-1` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 80

Calls

4 calls:

Slowest

14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
12.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
120.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
118.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
94.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.0s

Counts: 92 → 92

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.6b

localize194.0ms

Local error

Found 4 expressions with local error:

52.8b	(fma (- c) (* 4 a) (* c (* 4 a)))
52.8b	(fma (- c) (* 4 a) (* c (* 4 a)))
21.4b	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))
21.4b	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef` `hypot-def` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

Slowest

5.0ms	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))
5.0ms	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))
0.0ms	(fma (- c) (* 4 a) (* c (* 4 a)))
0.0ms	(fma (- c) (* 4 a) (* c (* 4 a)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))
143.0ms	(sqrt (+ (fma b b (- (* c (* 4 a)))) (fma (- c) (* 4 a) (* c (* 4 a)))))
35.0ms	(fma (- c) (* 4 a) (* c (* 4 a)))
31.0ms	(fma (- c) (* 4 a) (* c (* 4 a)))

simplify1.5s

Counts: 74 → 74

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.6b

regimes614.0ms

Accuracy

93.7% (0.8b remaining)

Error of 6.1b against oracle of 5.3b and baseline of 18.7b

bsearch330.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.1s	8715×	body	80	valid
1.1s	2811×	body	80	nan