Details

sample92.0ms

Algorithm

intervals

Results

22.0ms	205×	body	80	valid
15.0ms	31×	body	2560	valid
12.0ms	31×	body	1280	valid
7.0ms	89×	body	80	nan
4.0ms	12×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify187.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	164
6	164
5	160
4	153
3	121
2	64
1	29
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
60×	`prod-diff`
49×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r` `neg-log` `-commutative` `div-inv`

Counts

4 → 161

Calls

4 calls:

12.0ms	(* 4.0 (* a c))
85.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 4.0 (* a c))
127.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
130.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

173 → 173

Iterations

Iter	Nodes
done	5002
2	2609
1	639
0	253

prune888.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(* (* 4.0 a) c)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
60×	`prod-diff`
49×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-l` `neg-log` `-commutative` `div-inv`

Counts

4 → 161

Calls

4 calls:

86.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.0ms	(* (* 4.0 a) c)
47.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
32.0ms	(* (* 4.0 a) c)
104.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

173 → 173

Iterations

Iter	Nodes
done	5002
2	3168
1	658
0	256

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.2b	(* (* 4.0 a) c)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

125.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
13.0ms	(* (* 4.0 a) c)
45.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
35.0ms	(* (* 4.0 a) c)
130.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
134.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	3664
1	727
0	282

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(* (* 4.0 a) c)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
60×	`prod-diff`
49×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-l` `neg-log` `-commutative` `div-inv`

Counts

4 → 161

Calls

4 calls:

92.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms	(* (* 4.0 a) c)
24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.0ms	(* (* 4.0 a) c)
129.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

173 → 173

Iterations

Iter	Nodes
done	5002
2	3168
1	658
0	256

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

regimes413.0ms

Accuracy

87.1% (3.7b remaining)

Error of 9.0b against oracle of 5.3b and baseline of 34.1b

bsearch388.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	2.8233354537966034e+131
8	-8.904680992578465e-52	-2.849527055171251e-56	-5.546621280225112e-56
5	-1.0933554809811831e-44	-3.3311956001427126e-45	-3.4083546428522886e-45
7	-5.856362438573669e+138	-1.280729871585891e+137	-2.1229423973235387e+137

simplify17.0ms

Iterations

Iter	Nodes
done	49
1	49
0	41

end0.0ms

sample3.6s

Algorithm

intervals

Results

707.0ms	5841×	body	80	valid
606.0ms	1025×	body	2560	valid
564.0ms	2877×	body	80	nan
501.0ms	457×	body	640	valid
467.0ms	921×	body	1280	valid
68.0ms	122×	body	5120	valid
56.0ms	245×	body	320	valid
19.0ms	116×	body	160	valid