Details

sample204.0ms

Algorithm

intervals

Results

170.0ms

659×

body

valid

simplify902.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2009
4	2009
3	785
2	201
1	58
0	19

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
0.1b	(* (* a a) (+ 1 a))
0.3b	(* (* b b) (- 1 (* 3 a)))
0.3b	(pow (+ (* a a) (* b b)) 2)

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`add-cube-cbrt`
8×	`fma-def`
7×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
6×	`unpow-prod-down` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unpow2` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

96.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
43.0ms	(* (* a a) (+ 1 a))
41.0ms	(* (* b b) (- 1 (* 3 a)))
8.0ms	(pow (+ (* a a) (* b b)) 2)

series341.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
86.0ms	(* (* a a) (+ 1 a))
56.0ms	(* (* b b) (- 1 (* 3 a)))
47.0ms	(pow (+ (* a a) (* b b)) 2)

simplify1.1s

Counts

118 → 118

Iterations

Iter	Nodes
done	2000
2	2000
1	569
0	191

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (sqrt (+ (* a a) (* b b))) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
0.3b	(* (* b b) (- 1 (* 3 a)))
8.3b	(sqrt (+ (* a a) (* b b)))
8.3b	(sqrt (+ (* a a) (* b b)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`pow1`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`prod-diff` `sqrt-prod`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `hypot-def`
1×	`flip3--` `associate-l` `*-commutative` `fma-udef` `flip--` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (sqrt (+ (* a a) (* b b))) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
46.0ms	(* (* b b) (- 1 (* 3 a)))
8.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (sqrt (+ (* a a) (* b b))) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
67.0ms	(* (* b b) (- 1 (* 3 a)))
44.0ms	(sqrt (+ (* a a) (* b b)))
62.0ms	(sqrt (+ (* a a) (* b b)))

simplify1.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	2001
3	2001
2	1487
1	393
0	139

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (fma a a (* b b)) (fma a a (* b b))) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
0.1b	(* (* a a) (+ 1 a))
0.3b	(* (* b b) (- 1 (* 3 a)))
0.3b	(* (fma a a (* b b)) (fma a a (* b b)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
16×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`associate-r`
9×	`distribute-rgt-in` `distribute-lft-in`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`prod-diff` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-*r/` `fma-udef` `insert-posit16` `log1p-expm1-u`
3×	`swap-sqr` `*-commutative` `unswap-sqr`
2×	`associate-+l+` `associate-+r+` `sub-neg` `flip3-+` `flip-+`
1×	`pow2` `+-commutative` `sum-log` `fma-def` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out`

Counts

4 → 110

Calls

4 calls:

10.0ms	(+ (* (fma a a (* b b)) (fma a a (* b b))) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
36.0ms	(* (* a a) (+ 1 a))
52.0ms	(* (* b b) (- 1 (* 3 a)))
6.0ms	(* (fma a a (* b b)) (fma a a (* b b)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (* (fma a a (* b b)) (fma a a (* b b))) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
69.0ms	(* (* a a) (+ 1 a))
69.0ms	(* (* b b) (- 1 (* 3 a)))
74.0ms	(* (fma a a (* b b)) (fma a a (* b b)))

simplify1.1s

Counts

122 → 122

Iterations

Iter	Nodes
done	2004
2	2004
1	577
0	195

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))
0.3b	(* (* b b) (- 1 (* 3 a)))
8.3b	(sqrt (fma a a (* b b)))
8.3b	(sqrt (fma a a (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`pow1`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-prod`
7×	`associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `prod-diff`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`rem-sqrt-square` `sub-neg` `pow-plus` `associate-r/` `-commutative` `pow-prod-up` `hypot-def`
1×	`flip3--` `cube-unmult` `flip--`

Counts

4 → 100

Calls

4 calls:

7.0ms	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))
22.0ms	(* (* b b) (- 1 (* 3 a)))
1.0ms	(sqrt (fma a a (* b b)))
1.0ms	(sqrt (fma a a (* b b)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))
73.0ms	(* (* b b) (- 1 (* 3 a)))
67.0ms	(sqrt (fma a a (* b b)))
54.0ms	(sqrt (fma a a (* b b)))

simplify1.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	2005
3	2005
2	1055
1	341
0	134

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes234.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	30
1	30
0	20

end0.0ms

sample5.3s

Algorithm

intervals

Results

4.9s

20389×

body

valid