Details

sample103.0ms

Algorithm

intervals

Results

26.0ms	39×	body	2560	valid
21.0ms	186×	body	80	valid
14.0ms	29×	body	1280	valid
9.0ms	90×	body	80	nan
5.0ms	4×	body	160	valid
4.0ms	10×	body	640	valid
3.0ms	8×	body	320	valid
3.0ms	3×	body	5120	valid

simplify130.0ms

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: 32.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
1.0b	(- (* b b) (* (* 3 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite87.0ms

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:

30.0ms	(* (* 3 a) c)
17.0ms	(- (* b b) (* (* 3 a) c))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3 a) c)
72.0ms	(- (* b b) (* (* 3 a) c))
108.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
90.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.3s

Counts

96 → 96

Iterations

Iter	Nodes
3	3711
2	1102
1	350
0	138

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* -3 (* a c))
1.3b	(fma b b (* -3 (* a c)))
1.3b	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
21.7b	(sqrt (fma b b (* -3 (* a c))))

rewrite48.0ms

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:

30.0ms	(* -3 (* a c))
0.0ms	(fma b b (* -3 (* a c)))
14.0ms	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
2.0ms	(sqrt (fma b b (* -3 (* a c))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* -3 (* a c))
73.0ms	(fma b b (* -3 (* a c)))
132.0ms	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
110.0ms	(sqrt (fma b b (* -3 (* a c))))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
3	2329
2	742
1	269
0	116

prune958.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.8b

localize39.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

19.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
120.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
132.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
116.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
3	2519
2	743
1	231
0	88

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.8b

localize35.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))
21.7b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

19.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
20.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
121.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
95.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
115.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.9s

Counts

94 → 94

Iterations

Iter	Nodes
3	2519
2	743
1	231
0	88

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.8b

regimes651.0ms

Accuracy

84% (3.6b remaining)

Error of 14.6b against oracle of 11.0b and baseline of 33.6b

bsearch176.0ms

Steps

Iters	Range		Point
5	1.4610887943711312e+25	4.899560055505696e+25	1.487621333916267e+25
10	-1.0499721897563905e+163	-8.354690034354516e+151	-4.898678560179045e+152

simplify6.0ms

Iterations

Iter	Nodes
2	37
1	37
0	30

end0.0ms

sample4.3s

Algorithm

intervals

Results

932.0ms	1107×	body	2560	valid
893.0ms	5846×	body	80	valid
863.0ms	2917×	body	80	nan
628.0ms	933×	body	1280	valid
310.0ms	455×	body	640	valid
145.0ms	111×	body	5120	valid
85.0ms	111×	body	160	valid
72.0ms	211×	body	320	valid