Details

sample147.0ms

Algorithm

intervals

Results

39.0ms	32×	body	2560	valid
28.0ms	170×	body	80	valid
24.0ms	28×	body	1280	valid
14.0ms	20×	body	640	valid
12.0ms	78×	body	80	nan
4.0ms	4×	body	5120	valid
4.0ms	8×	body	320	valid
2.0ms	6×	body	160	valid

simplify249.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

249.0ms

(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize26.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma (* a c) -4 (* b b)))
2.7b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.4b	(fma (* a c) -4 (* b b))
0.1b	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
168×	`*-un-lft-identity`
159×	`times-frac`
116×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/l*`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`diff-log` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 240

Calls

4 calls:

Slowest

20.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
14.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series424.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
108.0ms	(sqrt (fma (* a c) -4 (* b b)))
95.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
72.0ms	(fma (* a c) -4 (* b b))

simplify30.0s

Counts

334 → 252

Calls

334 calls:

Slowest

431.0ms	(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
379.0ms	(/ (* (cbrt (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (cbrt (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2))) 1)
281.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
250.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
231.0ms	(fma (sqrt b) (- (sqrt b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune2.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.6b

localize21.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma (* a c) -4 (* b b)))
2.7b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.4b	(fma (* a c) -4 (* b b))
0.1b	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
168×	`*-un-lft-identity`
159×	`times-frac`
116×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/l*`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`diff-log` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 240

Calls

4 calls:

Slowest

32.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
10.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series384.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
98.0ms	(sqrt (fma (* a c) -4 (* b b)))
86.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
72.0ms	(fma (* a c) -4 (* b b))

simplify30.2s

Counts

334 → 252

Calls

334 calls:

Slowest

548.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
445.0ms	(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
282.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
256.0ms	(fma (sqrt b) (- (sqrt b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
245.0ms	(fma 1 (- b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune3.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize37.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma (* a c) -4 (* b b)))
2.7b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.4b	(fma (* a c) -4 (* b b))
0.2b	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

792×	`times-frac`
512×	`add-sqr-sqrt`
511×	`*-un-lft-identity`
363×	`add-cube-cbrt`
80×	`associate-/r*`
74×	`distribute-lft-out--` `difference-of-squares`
70×	`sqrt-prod`
60×	`prod-diff`
58×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
17×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1` `cbrt-undiv`
5×	`associate-/r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `associate-/l*`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

4 → 469

Calls

4 calls:

Slowest

34.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
20.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series430.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
114.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
92.0ms	(sqrt (fma (* a c) -4 (* b b)))
69.0ms	(fma (* a c) -4 (* b b))

simplify2.2m

Counts

724 → 481

Calls

724 calls:

Slowest

842.0ms	(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (/ (+ (sqrt (- b)) (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt 2))))
719.0ms	(/ (sqrt 1) (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
658.0ms	(/ (cbrt 1) (/ (cbrt a) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
650.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
571.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ 1 (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2)))))

prune6.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.6b

localize35.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma a (* c -4) (* b b)))
2.7b	(+ b (sqrt (fma a (* c -4) (* b b))))
0.2b	(fma a (* c -4) (* b b))
0.2b	(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`associate-r`
12×	`associate-l`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`add-log-exp`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u` `distribute-neg-frac`
3×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `distribute-lft-out`
2×	`frac-times` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`distribute-lft-neg-out` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sum-log` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 94

Calls

4 calls:

Slowest

44.0ms	(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
5.0ms	(+ b (sqrt (fma a (* c -4) (* b b))))
1.0ms	(sqrt (fma a (* c -4) (* b b)))
0.0ms	(fma a (* c -4) (* b b))

series394.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

110.0ms	(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
107.0ms	(sqrt (fma a (* c -4) (* b b)))
106.0ms	(+ b (sqrt (fma a (* c -4) (* b b))))
71.0ms	(fma a (* c -4) (* b b))

simplify4.1s

Counts

58 → 106

Calls

58 calls:

Slowest

366.0ms	(* (* (* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))
355.0ms	(* (+ (* b b) (- (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))) (* b (sqrt (fma a (* c -4) (* b b)))))) a)
290.0ms	(* (- (+ (pow b 3) (pow (sqrt (fma a (* c -4) (* b b))) 3))) (/ 1/2 a))
267.0ms	(* (* (* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)))
255.0ms	(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

regimes315.0ms

Accuracy

85.4% (4.1b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 33.6b

bsearch209.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.3s	874×	body	1280	valid
864.0ms	1087×	body	2560	valid
693.0ms	5812×	body	80	valid
460.0ms	2848×	body	80	nan
358.0ms	478×	body	640	valid
97.0ms	122×	body	5120	valid
77.0ms	236×	body	320	valid
46.0ms	118×	body	160	valid