Details

sample105.0ms

Algorithm

intervals

Results

84.0ms

682×

body

valid

simplify4.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	4855
5	1985
4	584
3	159
2	60
1	27
0	12

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(* 4 (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
0.4b	(pow (+ (* a a) (* b b)) 2)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`fma-def` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
8×	`add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

9.0ms	(+ (* a a) (* b b))
14.0ms	(* 4 (* b b))
77.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
16.0ms	(pow (+ (* a a) (* b b)) 2)

series258.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* a a) (* b b))
34.0ms	(* 4 (* b b))
108.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
50.0ms	(pow (+ (* a a) (* b b)) 2)

simplify3.9s

Counts

92 → 92

Iterations

Iter	Nodes
3	5648
2	1450
1	362
0	121

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (+ (* a a) (* b b)) 2)
0.4b	(pow (+ (* a a) (* b b)) 2)
15.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
15.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`pow-unpow` `unpow-prod-down` `add-exp-log` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

8.0ms	(pow (+ (* a a) (* b b)) 2)
9.0ms	(pow (+ (* a a) (* b b)) 2)
70.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
86.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (+ (* a a) (* b b)) 2)
53.0ms	(pow (+ (* a a) (* b b)) 2)
139.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
127.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

simplify953.0ms

Counts

90 → 90

Iterations

Iter	Nodes
3	2512
2	624
1	212
0	93

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

15.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`unpow-prod-down`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `unpow2` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 75

Calls

4 calls:

72.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
15.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
14.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
10.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))

series544.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
127.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
167.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
112.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))

simplify943.0ms

Counts

87 → 87

Iterations

Iter	Nodes
3	2247
2	612
1	220
0	102

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

15.1b	(sqrt (+ (* (* (cbrt (pow (+ (* a a) (* b b)) 2)) (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))) (cbrt (pow (+ (* a a) (* b b)) 2))) (* 4 (* b b))))
15.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))

rewrite493.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

424.0ms	(sqrt (+ (* (* (cbrt (pow (+ (* a a) (* b b)) 2)) (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))) (cbrt (pow (+ (* a a) (* b b)) 2))) (* 4 (* b b))))
47.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
13.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))

series638.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(sqrt (+ (* (* (cbrt (pow (+ (* a a) (* b b)) 2)) (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))) (cbrt (pow (+ (* a a) (* b b)) 2))) (* 4 (* b b))))
153.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
176.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
171.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))

simplify2.0s

Counts

86 → 86

Iterations

Iter	Nodes
3	3511
2	896
1	294
0	132

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes518.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	17
1	17
0	14

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.8s

20643×

body

valid