Details

sample115.0ms

Algorithm

intervals

Results

24.0ms	35×	body	2560	valid
22.0ms	184×	body	80	valid
18.0ms	86×	body	80	nan
16.0ms	28×	body	1280	valid
7.0ms	15×	body	640	valid
4.0ms	4×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify122.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
0.6b	(- (* b b) (* (* 3 a) c))
1.7b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
24.6b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

14.0ms	(* (* 3 a) c)
17.0ms	(- (* b b) (* (* 3 a) c))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* 3 a) c)
65.0ms	(- (* b b) (* (* 3 a) c))
110.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.6s

Counts

96 → 96

Iterations

Iter	Nodes
3	3711
2	1102
1	350
0	138

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.7b	(fma -3 (* c a) (* b b))
1.7b	(- (sqrt (fma -3 (* c a) (* b b))) b)
24.6b	(sqrt (fma -3 (* c a) (* b b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `fma-neg` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

30.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.0ms	(fma -3 (* c a) (* b b))
8.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
1.0ms	(sqrt (fma -3 (* c a) (* b b)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
77.0ms	(fma -3 (* c a) (* b b))
125.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
97.0ms	(sqrt (fma -3 (* c a) (* b b)))

simplify2.3s

Counts

114 → 114

Iterations

Iter	Nodes
3	3570
2	941
1	329
0	152

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
0.7b	(fma -3 (* c a) (* b b))
1.7b	(- (sqrt (fma -3 (* c a) (* b b))) b)
24.6b	(sqrt (fma -3 (* c a) (* b b)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

36.0ms	(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
0.0ms	(fma -3 (* c a) (* b b))
9.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
1.0ms	(sqrt (fma -3 (* c a) (* b b)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
62.0ms	(fma -3 (* c a) (* b b))
119.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
119.0ms	(sqrt (fma -3 (* c a) (* b b)))

simplify2.3s

Counts

191 → 191

Iterations

Iter	Nodes
3	4416
2	1410
1	600
0	278

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
0.7b	(fma -3 (* c a) (* b b))
1.7b	(- (sqrt (fma -3 (* c a) (* b b))) b)
24.6b	(sqrt (fma -3 (* c a) (* b b)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
30×	`add-cube-cbrt`
22×	`associate-r`
19×	`times-frac` `sqrt-prod`
18×	`prod-diff`
9×	`add-cbrt-cube` `add-exp-log`
8×	`difference-of-squares`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv` `flip--`

Counts

4 → 113

Calls

4 calls:

27.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
0.0ms	(fma -3 (* c a) (* b b))
22.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
2.0ms	(sqrt (fma -3 (* c a) (* b b)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
87.0ms	(fma -3 (* c a) (* b b))
120.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
120.0ms	(sqrt (fma -3 (* c a) (* b b)))

simplify1.7s

Counts

125 → 125

Iterations

Iter	Nodes
3	3254
2	1032
1	380
0	172

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.0b

regimes439.0ms

Accuracy

85% (3.4b remaining)

Error of 14.5b against oracle of 11.1b and baseline of 33.4b

bsearch191.0ms

Steps

Iters	Range		Point
8	2.5972983117194536e-74	3.3630379012102994e-71	3.32629031803127e-71
7	-1.8217288728729631e+111	-6.606823090402082e+109	-5.148407540792454e+110

simplify5.0ms

Iterations

Iter	Nodes
2	35
1	35
0	31

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.0s	1126×	body	2560	valid
899.0ms	2975×	body	80	nan
830.0ms	5836×	body	80	valid
716.0ms	915×	body	1280	valid
241.0ms	415×	body	640	valid
127.0ms	239×	body	320	valid
114.0ms	119×	body	5120	valid
28.0ms	114×	body	160	valid