Details

sample101.0ms

Algorithm

intervals

Results

22.0ms	190×	body	80	valid
21.0ms	32×	body	2560	valid
19.0ms	32×	body	1280	valid
9.0ms	79×	body	80	nan
6.0ms	12×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	5×	body	160	valid

simplify234.0ms

Counts: 1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize25.0ms

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)

rewrite40.0ms

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

24.0ms	(/ (/ (- (- 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))

series391.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
96.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
95.0ms	(sqrt (fma (* a c) -4 (* b b)))
77.0ms	(fma (* a c) -4 (* b b))

simplify994.0ms

Counts: 252 → 252

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.8b

localize46.0ms

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)

rewrite73.0ms

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

41.0ms	(/ (/ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 2) a)
21.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
3.0ms	(sqrt (fma -4 (* a c) (* b b)))
0.0ms	(fma -4 (* a c) (* b b))

series449.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
123.0ms	(sqrt (fma -4 (* a c) (* b b)))
108.0ms	(/ (/ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 2) a)
79.0ms	(fma -4 (* a c) (* b b))

simplify999.0ms

Counts: 252 → 252

prune3.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.8b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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

43.0ms	(* (- (- b) (sqrt (fma -4 (* c a) (* b b)))) (/ 1/2 a))
12.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
3.0ms	(sqrt (fma -4 (* c a) (* b b)))
0.0ms	(fma -4 (* c a) (* b b))

series402.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(* (- (- b) (sqrt (fma -4 (* c a) (* b b)))) (/ 1/2 a))
110.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
89.0ms	(sqrt (fma -4 (* c a) (* b b)))
86.0ms	(fma -4 (* c a) (* b b))

simplify2.3s

Counts: 173 → 173

prune2.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.7b

localize39.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma -4 (* c a) (* b b)))
20.7b	(sqrt (fma -4 (* c a) (* b b)))
20.7b	(sqrt (fma -4 (* c a) (* b b)))
1.7b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 139

Calls

4 calls:

Slowest

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

series421.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(sqrt (fma -4 (* c a) (* b b)))
105.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
104.0ms	(sqrt (fma -4 (* c a) (* b b)))
102.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.4s

Counts: 151 → 151

prune2.3s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 5.7b

regimes571.0ms

Accuracy

84.7% (4.2b remaining)

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

bsearch233.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.5s	5896×	body	80	valid
1.1s	1071×	body	2560	valid
843.0ms	2903×	body	80	nan
783.0ms	895×	body	1280	valid
386.0ms	475×	body	640	valid
211.0ms	105×	body	5120	valid
135.0ms	239×	body	320	valid
27.0ms	99×	body	160	valid