Details

sample117.0ms

Algorithm

intervals

Results

27.0ms	36×	body	2560	valid
26.0ms	187×	body	80	valid
17.0ms	25×	body	1280	valid
13.0ms	86×	body	80	nan
9.0ms	17×	body	640	valid
3.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify135.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize29.0ms

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)))

rewrite78.0ms

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:

31.0ms	(* (* 3 a) c)
16.0ms	(- (* b b) (* (* 3 a) c))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 3 a) c)
88.0ms	(- (* b b) (* (* 3 a) c))
109.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
130.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.0s

Counts

96 → 96

Iterations

Iter	Nodes
done	2000
3	2000
2	1086
1	352
0	138

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.6b

localize32.0ms

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))))

rewrite40.0ms

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:

22.0ms	(* -3 (* a c))
16.0ms	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
0.0ms	(fma b b (* -3 (* a c)))
1.0ms	(sqrt (fma b b (* -3 (* a c))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* -3 (* a c))
123.0ms	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
62.0ms	(fma b b (* -3 (* a c)))
134.0ms	(sqrt (fma b b (* -3 (* a c))))

simplify927.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
3	2000
2	776
1	271
0	116

prune957.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.5b

localize53.0ms

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)))))

rewrite50.0ms

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:

29.0ms	(* (cbrt -3) (* a c))
16.0ms	(+ (- 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))))
3.0ms	(sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c)))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cbrt -3) (* a c))
199.0ms	(+ (- b) (sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c))))))
141.0ms	(fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c))))
178.0ms	(sqrt (fma b b (* (* (cbrt -3) (cbrt -3)) (* (cbrt -3) (* a c)))))

simplify938.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	2026
3	2026
2	826
1	282
0	122

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 13.5b

localize39.0ms

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)))

rewrite70.0ms

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:

15.0ms	(- (* b b) (* (* 3 a) c))
15.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
16.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 3 a) c))
88.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
93.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
101.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify866.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	2003
3	2003
2	886
1	282
0	109

prune1.0s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 13.5b

regimes618.0ms

Accuracy

85.5% (3.1b remaining)

Error of 14.8b against oracle of 11.8b and baseline of 32.9b

bsearch202.0ms

Steps

Iters	Range		Point
8	5.833527798943191e-77	3.6732813120885656e-72	6.235673785124529e-73
7	-2.005420514903704e+154	-2.9230384601346835e+152	-1.3376190644449892e+154

simplify5.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	5891×	body	80	valid
814.0ms	1025×	body	2560	valid
600.0ms	882×	body	1280	valid
441.0ms	2952×	body	80	nan
262.0ms	462×	body	640	valid
139.0ms	96×	body	5120	valid
81.0ms	238×	body	320	valid
23.0ms	104×	body	160	valid