Details

sample131.0ms

Algorithm

intervals

Results

90.0ms

665×

body

valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	179	28
3	594	28
4	2383	28
done	5000	28

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.1b	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.4b	(pow (fma a a (* b b)) 2.0)
1.0b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`pow-to-exp` `flip3--` `pow-pow` `associate-l` `pow-exp` `*-commutative` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
3.0ms	(pow (fma a a (* b b)) 2.0)
54.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
167.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
199.0ms	(pow (fma a a (* b b)) 2.0)
66.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.3s

Counts

84 → 84

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	160	1452
1	429	1415
2	2544	1221
done	5002	1210

prune452.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* b b) (- 1.0 (* 3.0 a)))
1.0b	(* (* b b) (- 1.0 (* 3.0 a)))
6.3b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.3b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `prod-diff`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

31.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
59.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
3.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series723.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
82.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
284.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
283.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify2.1s

Counts

108 → 108

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	130	2220
1	348	2078
2	2062	1852
done	5000	1820

prune635.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* b b) (- 1.0 (* 3.0 a)))
6.3b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.8b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.8b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

40.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
300.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
346.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
380.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify2.4s

Counts

86 → 86

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	181	2406
1	465	2325
2	2417	2090
done	5001	2030

prune632.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.3b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.3b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.8b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 58

Calls

4 calls:

3.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
3.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
3.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
2.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

336.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
273.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
315.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
351.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify2.1s

Counts

70 → 70

Iterations

Useful iterations: 3 (856.0ms)

Iter	Nodes	Cost
0	116	2361
1	253	2158
2	734	2000
3	3124	1959
done	5001	1959

prune678.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes292.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	28
1	20	28
done	20	28

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.9s

20473×

body

valid