Details

sample82.0ms

Algorithm

intervals

Results

21.0ms	36×	body	2560	valid
18.0ms	187×	body	80	valid
12.0ms	25×	body	1280	valid
8.0ms	86×	body	80	nan
7.0ms	17×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
0.8b	(- (* b b) (* (* 3 a) c))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
23.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite54.0ms

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:

20.0ms	(* (* 3 a) c)
10.0ms	(- (* b b) (* (* 3 a) c))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (* 3 a) c)
78.0ms	(- (* b b) (* (* 3 a) c))
102.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
78.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.2s

Counts

96 → 96

Iterations

Iter	Nodes
3	3711
2	1102
1	350
0	138

prune680.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* -3 (* a c))
0.9b	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
1.0b	(fma b b (* -3 (* a c)))
23.5b	(sqrt (fma b b (* -3 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

13.0ms	(* -3 (* a c))
13.0ms	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
0.0ms	(fma b b (* -3 (* a c)))
2.0ms	(sqrt (fma b b (* -3 (* a c))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* -3 (* a c))
115.0ms	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
56.0ms	(fma b b (* -3 (* a c)))
121.0ms	(sqrt (fma b b (* -3 (* a c))))

simplify779.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2300
2	746
1	269
0	116

prune544.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt -3) (* a c))
0.9b	(+ (- b) (sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c))))))
1.0b	(fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c))))
23.5b	(sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

39.0ms	(* (cbrt -3) (* a c))
17.0ms	(+ (- b) (sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c))))))
0.0ms	(fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c))))
2.0ms	(sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c)))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cbrt -3) (* a c))
186.0ms	(+ (- b) (sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c))))))
159.0ms	(fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c))))
203.0ms	(sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c)))))

simplify1.0s

Counts

91 → 91

Iterations

Iter	Nodes
3	2314
2	794
1	280
0	122

prune563.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 12.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3 a) c))
11.4b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 3 a) c)))
23.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

17.0ms	(- (* b b) (* (* 3 a) c))
25.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
20.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* b b) (* (* 3 a) c))
119.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
101.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
101.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.6s

Counts

91 → 91

Iterations

Iter	Nodes
3	2793
2	883
1	280
0	109

prune523.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 12.5b

regimes641.0ms

Accuracy

85.5% (3.2b remaining)

Error of 14.1b against oracle of 10.9b and baseline of 32.9b

bsearch192.0ms

Steps

Iters	Range		Point
8	5.833527798943191e-77	3.6732813120885656e-72	3.602826357305206e-72
9	-2.2464591800446616e+91	-3.153507839293123e+86	-1.3599228730895225e+90

simplify11.0ms

Iterations

Iter	Nodes
2	36
1	36
0	30

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.1s	882×	body	1280	valid
848.0ms	1025×	body	2560	valid
840.0ms	5891×	body	80	valid
532.0ms	2952×	body	80	nan
322.0ms	462×	body	640	valid
115.0ms	238×	body	320	valid
82.0ms	96×	body	5120	valid
24.0ms	104×	body	160	valid