Details

sample133.0ms

Algorithm

intervals

Results

45.0ms	190×	body	80	valid
23.0ms	32×	body	2560	valid
22.0ms	32×	body	1280	valid
11.0ms	79×	body	80	nan
7.0ms	12×	body	640	valid
4.0ms	11×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	5×	body	160	valid

simplify234.0ms

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize46.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma (* a c) -4 (* b b)))
1.7b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.4b	(fma (* a c) -4 (* b b))
0.1b	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite81.0ms

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

40.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
28.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
4.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(fma (* a c) -4 (* b b))

series430.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
120.0ms	(sqrt (fma (* a c) -4 (* b b)))
98.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
79.0ms	(fma (* a c) -4 (* b b))

simplify895.0ms

Counts: 252 → 252

prune2.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.8b

localize22.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma -4 (* a c) (* b b)))
1.7b	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.4b	(fma -4 (* a c) (* b b))
0.1b	(/ (/ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 2) a)

rewrite45.0ms

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

25.0ms	(/ (/ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 2) a)
14.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))
0.0ms	(fma -4 (* a c) (* b b))

series398.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(/ (/ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 2) a)
97.0ms	(sqrt (fma -4 (* a c) (* b b)))
93.0ms	(fma -4 (* a c) (* b b))
91.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))

simplify978.0ms

Counts: 252 → 252

prune3.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.8b

localize28.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma -4 (* a c) (* b b)))
1.7b	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.4b	(fma -4 (* a c) (* b b))
0.2b	(* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) (/ 1/2 a))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
10×	`times-frac` `fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 161

Calls

4 calls:

Slowest

45.0ms	(* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) (/ 1/2 a))
11.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))
0.0ms	(fma -4 (* a c) (* b b))

series430.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

138.0ms	(* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) (/ 1/2 a))
101.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
97.0ms	(sqrt (fma -4 (* a c) (* b b)))
95.0ms	(fma -4 (* a c) (* b b))

simplify2.2s

Counts: 173 → 173

prune2.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.7b

localize40.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma -4 (* a c) (* b b)))
1.7b	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.4b	(fma -4 (* a c) (* b b))
0.1b	(/ (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2) a)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
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`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 144

Calls

4 calls:

Slowest

46.0ms	(/ (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2) a)
20.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
2.0ms	(sqrt (fma -4 (* a c) (* b b)))
0.0ms	(fma -4 (* a c) (* b b))

series450.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

152.0ms	(/ (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2) a)
125.0ms	(sqrt (fma -4 (* a c) (* b b)))
92.0ms	(fma -4 (* a c) (* b b))
81.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))

simplify2.7s

Counts: 156 → 156

prune1.9s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.7b

regimes417.0ms

Accuracy

84.7% (4.2b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 33.4b

bsearch194.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	1071×	body	2560	valid
932.0ms	5896×	body	80	valid
756.0ms	895×	body	1280	valid
376.0ms	2903×	body	80	nan
320.0ms	475×	body	640	valid
168.0ms	105×	body	5120	valid
91.0ms	239×	body	320	valid
26.0ms	99×	body	160	valid