Details

sample84.0ms

Algorithm

intervals

Results

24.0ms	29×	body	1280	valid
17.0ms	36×	body	2560	valid
16.0ms	184×	body	80	valid
6.0ms	77×	body	80	nan
3.0ms	10×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	4×	body	5120	valid
1.0ms	4×	body	160	valid

simplify496.0ms

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.2b	(- (* b b) (* (* 3 a) c))
23.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite64.0ms

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:

25.0ms	(* (* 3 a) c)
16.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
8.0ms	(- (* b b) (* (* 3 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* 3 a) c)
109.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
80.0ms	(- (* b b) (* (* 3 a) c))
116.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.1s

Counts

96 → 96

Iterations

Iter	Nodes
3	3759
2	1097
1	351
0	138

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
1.1b	(- (sqrt (fma -3 (* c a) (* b b))) b)
1.3b	(fma -3 (* c a) (* b b))
23.1b	(sqrt (fma -3 (* c a) (* b b)))

rewrite32.0ms

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:

22.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
7.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
0.0ms	(fma -3 (* c a) (* b b))
1.0ms	(sqrt (fma -3 (* c a) (* b b)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
104.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
76.0ms	(fma -3 (* c a) (* b b))
81.0ms	(sqrt (fma -3 (* c a) (* b b)))

simplify2.0s

Counts

114 → 114

Iterations

Iter	Nodes
3	3112
2	898
1	329
0	152

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
1.1b	(- (sqrt (fma -3 (* c a) (* b b))) b)
1.3b	(fma -3 (* c a) (* b b))
23.1b	(sqrt (fma -3 (* c a) (* b b)))

rewrite40.0ms

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:

26.0ms	(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
7.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
0.0ms	(fma -3 (* c a) (* b b))
1.0ms	(sqrt (fma -3 (* c a) (* b b)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
117.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
95.0ms	(fma -3 (* c a) (* b b))
138.0ms	(sqrt (fma -3 (* c a) (* b b)))

simplify2.4s

Counts

191 → 191

Iterations

Iter	Nodes
3	4349
2	1410
1	600
0	278

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (/ 1/3 a))
0.3b	(/ 1/3 a)
1.1b	(- (sqrt (fma c (* -3 a) (* b b))) b)
23.1b	(sqrt (fma c (* -3 a) (* b b)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`add-cube-cbrt`
19×	`times-frac`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `flip3--` `flip--` `associate-/l`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 130

Calls

4 calls:

45.0ms	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (/ 1/3 a))
4.0ms	(/ 1/3 a)
8.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -3 a) (* b b)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (/ 1/3 a))
31.0ms	(/ 1/3 a)
122.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
100.0ms	(sqrt (fma c (* -3 a) (* b b)))

simplify1.5s

Counts

142 → 142

Iterations

Iter	Nodes
3	3249
2	1027
1	379
0	181

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.4b

regimes409.0ms

Accuracy

84.8% (3.3b remaining)

Error of 15.2b against oracle of 12.0b and baseline of 33.4b

bsearch185.0ms

Steps

Iters	Range		Point
10	8.951341119180922e-71	6.02619389320856e-56	2.1188761372830013e-69
9	-1.0070153765052194e+149	-1.0895875309198726e+143	-1.877074429265673e+148

simplify5.0ms

Iterations

Iter	Nodes
2	32
1	32
0	29

end0.0ms

sample3.8s

Algorithm

intervals

Results

884.0ms	1115×	body	2560	valid
862.0ms	5822×	body	80	valid
567.0ms	910×	body	1280	valid
455.0ms	109×	body	5120	valid
349.0ms	2907×	body	80	nan
244.0ms	419×	body	640	valid
73.0ms	229×	body	320	valid
23.0ms	102×	body	160	valid