Details

sample66.0ms

Algorithm

intervals

Results

19.0ms	258×	body	80	valid
4.0ms	14×	body	640	valid
3.0ms	9×	body	1280	valid
3.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify9.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	322	12
5	766	12
6	1555	12
7	2873	12
8	4761	12
done	5000	12

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
4.2b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite60.0ms

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:

57.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series286.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (- y z) (- a z))
218.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify1.7s

Counts

70 → 70

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	116	918
1	266	890
2	653	838
3	1707	834
done	5001	830

prune370.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.1b	(/ 1 (/ (- a z) (- y z)))
4.2b	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

49.0ms	(/ (- a z) (- y z))
53.0ms	(/ 1 (/ (- a z) (- y z)))
0.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

series572.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(/ (- a z) (- y z))
231.0ms	(/ 1 (/ (- a z) (- y z)))
238.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

simplify2.8s

Counts

223 → 223

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	273	3782
1	615	3270
2	1414	2947
3	3930	2867
done	5002	2865

prune609.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.0b	(/ 1 (- y z))
0.2b	(/ (/ 1 (- a z)) (/ 1 (- y z)))
4.2b	(fma (/ (/ 1 (- a z)) (/ 1 (- y z))) (- t x) x)

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

1131×	`times-frac`
700×	`add-sqr-sqrt` `*-un-lft-identity`
420×	`add-cube-cbrt`
140×	`distribute-lft-out--` `difference-of-squares`
93×	`associate-/r/`
52×	`add-exp-log`
47×	`div-inv`
46×	`flip3--` `flip--`
36×	`div-exp`
31×	`associate-/r*`
27×	`associate-/l*`
20×	`add-cbrt-cube`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`fma-udef` `associate-/l/`

Counts

4 → 613

Calls

4 calls:

13.0ms	(/ 1 (- a z))
19.0ms	(/ 1 (- y z))
52.0ms	(/ (/ 1 (- a z)) (/ 1 (- y z)))
1.0ms	(fma (/ (/ 1 (- a z)) (/ 1 (- y z))) (- t x) x)

series523.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 1 (- a z))
71.0ms	(/ 1 (- y z))
185.0ms	(/ (/ 1 (- a z)) (/ 1 (- y z)))
206.0ms	(fma (/ (/ 1 (- a z)) (/ 1 (- y z))) (- t x) x)

simplify2.1s

Counts

625 → 625

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	750	15076
1	2066	11234
2	3807	9996
done	5000	9994

prune976.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
8.8b	(fma (* (* (cbrt (- y z)) (cbrt (- y z))) (/ (cbrt (- y z)) (- a z))) (- t x) x)

rewrite24.0ms

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 (- y z))
4.0ms	(cbrt (- y z))
5.0ms	(cbrt (- y z))
1.0ms	(fma (* (* (cbrt (- y z)) (cbrt (- y z))) (/ (cbrt (- y z)) (- a z))) (- t x) x)

series818.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt (- y z))
218.0ms	(cbrt (- y z))
198.0ms	(cbrt (- y z))
158.0ms	(fma (* (* (cbrt (- y z)) (cbrt (- y z))) (/ (cbrt (- y z)) (- a z))) (- t x) x)

simplify3.6s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	96	925
1	198	907
2	435	749
3	1162	676
4	4176	636
done	5000	636

prune410.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes450.0ms

Accuracy

28% (6.3b remaining)

Error of 9.6b against oracle of 3.2b and baseline of 12.0b

bsearch176.0ms

Steps

Iters	Range		Point
8	1.4707725137908467e-101	8.579273971687159e-98	4.148123673034126e-100
9	-6.52872999559967e-121	-1.2083430315066995e-126	-5.991117286694601e-124

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	63
1	29	63
done	29	63

end0.0ms

sample1.8s

Algorithm

intervals

Results

753.0ms	7897×	body	80	valid
143.0ms	469×	body	640	valid
114.0ms	264×	body	1280	valid
68.0ms	373×	body	320	valid
33.0ms	275×	body	160	valid
8.0ms	21×	body	2560	valid