Details

sample141.0ms

Algorithm

intervals

Results

117.0ms

659×

body

valid

simplify817.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2160
3	649
2	198
1	56
0	19

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

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)

rewrite112.0ms

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:

49.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
23.0ms	(* (* a a) (+ 1 a))
26.0ms	(* (* b b) (- 1 (* 3 a)))
12.0ms	(pow (+ (* a a) (* b b)) 2)

series295.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
58.0ms	(* (* a a) (+ 1 a))
61.0ms	(* (* b b) (- 1 (* 3 a)))
49.0ms	(pow (+ (* a a) (* b b)) 2)

simplify22.3s

Counts

118 → 118

Iterations

Iter	Nodes
3	8662
2	1927
1	542
0	191

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

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)))

rewrite65.0ms

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))))))
45.0ms	(* (* b b) (- 1 (* 3 a)))
11.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(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))))))
81.0ms	(* (* b b) (- 1 (* 3 a)))
56.0ms	(sqrt (+ (* a a) (* b b)))
53.0ms	(sqrt (+ (* a a) (* b b)))

simplify8.0s

Counts

95 → 95

Iterations

Iter	Nodes
3	4934
2	1347
1	391
0	139

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a a) (+ 1 a))
0.2b	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (hypot a 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)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

24.0ms	(* (* a a) (+ 1 a))
0.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (hypot a b) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
58.0ms	(* (* b b) (- 1 (* 3 a)))
14.0ms	(sqrt (+ (* a a) (* b b)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* a a) (+ 1 a))
241.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (hypot a b) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
75.0ms	(* (* b b) (- 1 (* 3 a)))
44.0ms	(sqrt (+ (* a a) (* b b)))

simplify14.6s

Counts

103 → 103

Iterations

Iter	Nodes
3	6360
2	1810
1	518
0	179

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (+ 1 a)) (cbrt (+ 1 a)))
0.2b	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (hypot a b) 2) (* 4 (+ (* (* (* a a) (* (cbrt (+ 1 a)) (cbrt (+ 1 a)))) (cbrt (+ 1 a))) (* (* b b) (- 1 (* 3 a))))))
0.3b	(* (* b b) (- 1 (* 3 a)))
8.3b	(sqrt (+ (* a a) (* b b)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`cbrt-prod`
17×	`pow1`
16×	`add-cube-cbrt`
12×	`cbrt-div`
11×	`add-exp-log`
10×	`associate-r`
9×	`add-cbrt-cube` `swap-sqr`
8×	`associate-l`
7×	`flip3-+` `flip-+`
6×	`pow1/3` `prod-diff` `distribute-lft-out`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `associate-*r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`sub-neg` `sqrt-div` `associate-l/` `pow-sqr` `-commutative` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--`

Counts

4 → 120

Calls

4 calls:

23.0ms	(* (cbrt (+ 1 a)) (cbrt (+ 1 a)))
0.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (hypot a b) 2) (* 4 (+ (* (* (* a a) (* (cbrt (+ 1 a)) (cbrt (+ 1 a)))) (cbrt (+ 1 a))) (* (* b b) (- 1 (* 3 a))))))
27.0ms	(* (* b b) (- 1 (* 3 a)))
6.0ms	(sqrt (+ (* a a) (* b b)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (cbrt (+ 1 a)) (cbrt (+ 1 a)))
172.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2) (pow (hypot a b) 2) (* 4 (+ (* (* (* a a) (* (cbrt (+ 1 a)) (cbrt (+ 1 a)))) (cbrt (+ 1 a))) (* (* b b) (- 1 (* 3 a))))))
54.0ms	(* (* b b) (- 1 (* 3 a)))
38.0ms	(sqrt (+ (* a a) (* b b)))

simplify10.3s

Counts

132 → 132

Iterations

Iter	Nodes
3	6254
2	1856
1	573
0	223

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes144.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	33
1	33
0	25

end0.0ms

sample3.4s

Algorithm

intervals

Results

3.1s

20389×

body

valid