Details

sample73.0ms

Algorithm

intervals

Results

34.0ms

524×

body

valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 4 (183.0ms)

Iter	Nodes	Cost
0	11	13
1	21	13
2	52	13
3	171	13
4	496	12
5	1885	12
done	5001	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- t (* z z))
6.6b	(fma (* y 4.0) (- t (* z z)) (* x x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `difference-of-squares`

Counts

2 → 31

Calls

2 calls:

6.0ms	(- t (* z z))
0.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))

series227.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(- t (* z z))
167.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))

simplify615.0ms

Counts

37 → 37

Iterations

Useful iterations: done (613.0ms)

Iter	Nodes	Cost
0	65	421
1	155	415
2	639	357
done	5000	349

prune168.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 4 expressions with local error:

6.6b	(fma (* y 4.0) (* (* (cbrt (- t (* z z))) (cbrt (- t (* z z)))) (cbrt (- t (* z z)))) (* x x))
7.2b	(cbrt (- t (* z z)))
7.2b	(cbrt (- t (* z z)))
7.2b	(cbrt (- t (* z z)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

0.0ms	(fma (* y 4.0) (* (* (cbrt (- t (* z z))) (cbrt (- t (* z z)))) (cbrt (- t (* z z)))) (* x x))
3.0ms	(cbrt (- t (* z z)))
3.0ms	(cbrt (- t (* z z)))
3.0ms	(cbrt (- t (* z z)))

series1.4s

Counts

4 → 12

Calls

4 calls:

163.0ms	(fma (* y 4.0) (* (* (cbrt (- t (* z z))) (cbrt (- t (* z z)))) (cbrt (- t (* z z)))) (* x x))
431.0ms	(cbrt (- t (* z z)))
413.0ms	(cbrt (- t (* z z)))
415.0ms	(cbrt (- t (* z z)))

simplify3.1s

Counts

70 → 70

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	97	1117
1	221	1087
2	734	834
3	4171	770
done	5000	767

prune414.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.1b

localize42.0ms

Local error

Found 4 expressions with local error:

7.2b	(cbrt (- t (* z z)))
7.2b	(cbrt (- t (* z z)))
7.2b	(cbrt (- t (* z z)))
7.2b	(cbrt (- t (* z z)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

3.0ms	(cbrt (- t (* z z)))
3.0ms	(cbrt (- t (* z z)))
4.0ms	(cbrt (- t (* z z)))
4.0ms	(cbrt (- t (* z z)))

series1.7s

Counts

4 → 12

Calls

4 calls:

434.0ms	(cbrt (- t (* z z)))
464.0ms	(cbrt (- t (* z z)))
423.0ms	(cbrt (- t (* z z)))
369.0ms	(cbrt (- t (* z z)))

simplify1.5s

Counts

76 → 76

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	73	952
1	165	912
2	449	840
3	1507	796
done	5000	760

prune504.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.1b

localize28.0ms

Local error

Found 4 expressions with local error:

1.9b	(cbrt (fma (* y 4.0) (- t (* z z)) (* x x)))
6.6b	(fma (* y 4.0) (- t (* z z)) (* x x))
6.6b	(fma (* y 4.0) (- t (* z z)) (* x x))
6.6b	(fma (* y 4.0) (- t (* z z)) (* x x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

2.0ms	(cbrt (fma (* y 4.0) (- t (* z z)) (* x x)))
1.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))
1.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))
1.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))

series887.0ms

Counts

4 → 12

Calls

4 calls:

510.0ms	(cbrt (fma (* y 4.0) (- t (* z z)) (* x x)))
127.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))
134.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))
116.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))

simplify1.1s

Counts

55 → 55

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	70	924
1	142	920
2	417	799
3	1788	781
done	5001	775

prune220.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 6.1b

regimes348.0ms

Accuracy

0% (0.7b remaining)

Error of 5.9b against oracle of 5.2b and baseline of 5.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
done	11	12

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

15934×

body

valid