Details

sample35.0ms

Algorithm

intervals

Results

14.0ms

498×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (84.0ms)

Iter	Nodes	Cost
0	11	13
1	21	13
2	52	13
3	171	13
4	346	12
5	586	12
6	698	12
7	805	12
8	1042	12
9	1225	12
10	1228	12
done	1228	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
0.0b	(- (* z z) t)
5.5b	(* (* y 4.0) (- (* z z) t))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

16×	`prod-diff`
11×	`add-sqr-sqrt`
10×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`sub-neg`
4×	`associate-r`
3×	`expm1-log1p-u` `flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u`
2×	`fma-neg` `diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 78

Calls

3 calls:

12.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
13.0ms	(- (* z z) t)
39.0ms	(* (* y 4.0) (- (* z z) t))

series203.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
24.0ms	(- (* z z) t)
79.0ms	(* (* y 4.0) (- (* z z) t))

simplify1.1s

Counts

87 → 87

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	148	1288
1	390	1137
2	1271	994
done	5001	966

prune226.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- t (pow z 2))
5.5b	(* (* y 4.0) (- t (pow z 2)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
58×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
29×	`unpow-prod-down`
26×	`distribute-rgt-in` `distribute-lft-in`
11×	`unpow2` `sqr-pow`
8×	`associate-r` `difference-of-squares`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`sub-neg` `fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 125

Calls

2 calls:

12.0ms	(- t (pow z 2))
50.0ms	(* (* y 4.0) (- t (pow z 2)))

series158.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- t (pow z 2))
106.0ms	(* (* y 4.0) (- t (pow z 2)))

simplify1.3s

Counts

131 → 131

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	218	3431
1	510	2500
2	1367	1887
done	5001	1538

prune198.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma x x (* t (* y 4.0)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma x x (* t (* y 4.0)))

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

(fma x x (* t (* y 4.0)))

simplify3.6s

Counts

13 → 13

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	22	138
1	35	135
2	73	135
3	221	119
4	803	119
5	4362	119
done	5000	119

prune45.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma x x (* t (* y 4.0)))) (cbrt (fma x x (* t (* y 4.0)))))
3.7b	(cbrt (fma x x (* t (* y 4.0))))
3.7b	(cbrt (fma x x (* t (* y 4.0))))
3.7b	(cbrt (fma x x (* t (* y 4.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

11.0ms	(* (cbrt (fma x x (* t (* y 4.0)))) (cbrt (fma x x (* t (* y 4.0)))))
1.0ms	(cbrt (fma x x (* t (* y 4.0))))
1.0ms	(cbrt (fma x x (* t (* y 4.0))))
1.0ms	(cbrt (fma x x (* t (* y 4.0))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (cbrt (fma x x (* t (* y 4.0)))) (cbrt (fma x x (* t (* y 4.0)))))
111.0ms	(cbrt (fma x x (* t (* y 4.0))))
111.0ms	(cbrt (fma x x (* t (* y 4.0))))
109.0ms	(cbrt (fma x x (* t (* y 4.0))))

simplify2.1s

Counts

93 → 93

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	95	1710
1	194	1593
2	482	1460
3	1160	1264
4	3043	1225
done	5001	1163

prune264.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.7b

regimes455.0ms

Accuracy

84.1% (0.5b remaining)

Error of 3.1b against oracle of 2.5b and baseline of 6.0b

bsearch151.0ms

Steps

Iters	Range		Point
9	2.2797593729061864e+144	4.0038839218266663e+151	3.942332962792774e+151
10	-1.7625656646217042e+172	-3.226459196029535e+159	-3.2627604844150644e+159

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	55
1	34	55
done	34	55

end0.0ms

sample1.0s

Algorithm

intervals

Results

467.0ms

16040×

body

valid