Details

sample40.0ms

Algorithm

intervals

Results

15.0ms	274×	body	80	valid
0.0ms	1×	body	640	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	10	11
1	20	11
2	36	10
3	59	10
4	102	10
5	161	10
6	212	10
7	240	10
8	278	10
9	319	10
10	404	10
11	502	10
12	570	10
13	634	10
14	662	10
done	662	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.6b	(fma (/ (- z t) (- a t)) y x)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

26.0ms	(/ (- z t) (- a t))
0.0ms	(fma (/ (- z t) (- a t)) y x)

series169.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (- z t) (- a t))
101.0ms	(fma (/ (- z t) (- a t)) y x)

simplify2.9s

Counts

70 → 70

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	113	884
1	259	856
2	632	808
3	1589	808
4	4609	806
done	5000	806

prune268.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.8b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b	(fma (* (* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t)))) (cbrt (/ (- z t) (- a t)))) y x)
4.0b	(cbrt (/ (- z t) (- a t)))
4.0b	(cbrt (/ (- z t) (- a t)))
4.0b	(cbrt (/ (- z t) (- a t)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 136

Calls

4 calls:

0.0ms	(fma (* (* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t)))) (cbrt (/ (- z t) (- a t)))) y x)
10.0ms	(cbrt (/ (- z t) (- a t)))
10.0ms	(cbrt (/ (- z t) (- a t)))
10.0ms	(cbrt (/ (- z t) (- a t)))

series1.5s

Counts

4 → 12

Calls

4 calls:

97.0ms	(fma (* (* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t)))) (cbrt (/ (- z t) (- a t)))) y x)
453.0ms	(cbrt (/ (- z t) (- a t)))
413.0ms	(cbrt (/ (- z t) (- a t)))
541.0ms	(cbrt (/ (- z t) (- a t)))

simplify3.3s

Counts

148 → 148

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	175	2777
1	332	2684
2	669	2387
3	1555	2330
4	4263	2264
done	5000	2261

prune799.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
1.6b	(fma (/ (* (cbrt (- z t)) (cbrt (- z t))) (/ (- a t) (cbrt (- z t)))) y x)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
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--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

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

series769.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(cbrt (- z t))
224.0ms	(cbrt (- z t))
220.0ms	(cbrt (- z t))
117.0ms	(fma (/ (* (cbrt (- z t)) (cbrt (- z t))) (/ (- a t) (cbrt (- z t)))) y x)

simplify2.4s

Counts

73 → 73

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	93	891
1	194	873
2	411	719
3	986	647
4	2888	611
done	5001	599

prune388.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (/ (- z t) (- a t)) y x))
1.6b	(fma (/ (- z t) (- a t)) y x)
1.6b	(fma (/ (- z t) (- a t)) y x)
1.6b	(fma (/ (- z t) (- a t)) y x)

rewrite4.0ms

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 (/ (- z t) (- a t)) y x))
1.0ms	(fma (/ (- z t) (- a t)) y x)
1.0ms	(fma (/ (- z t) (- a t)) y x)
1.0ms	(fma (/ (- z t) (- a t)) y x)

series1.1s

Counts

4 → 12

Calls

4 calls:

784.0ms	(cbrt (fma (/ (- z t) (- a t)) y x))
113.0ms	(fma (/ (- z t) (- a t)) y x)
99.0ms	(fma (/ (- z t) (- a t)) y x)
112.0ms	(fma (/ (- z t) (- a t)) y x)

simplify2.8s

Counts

55 → 55

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	60	737
1	119	732
2	276	647
3	891	641
4	3360	633
done	5001	629

prune307.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.8b

regimes351.0ms

Accuracy

0% (0.6b remaining)

Error of 1.4b against oracle of 0.8b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
done	9	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

598.0ms	8687×	body	80	valid
0.0ms	2×	body	640	valid