Details

sample41.0ms

Algorithm

intervals

Results

13.0ms	233×	body	80	valid
4.0ms	17×	body	640	valid
3.0ms	10×	body	1280	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	2×	body	2560	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (72.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	110	13
4	239	12
5	729	12
6	3426	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.9b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite47.0ms

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:

44.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series331.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- t z) (- a t))
272.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.7s

Counts

70 → 70

Iterations

Useful iterations: 3 (930.0ms)

Iter	Nodes	Cost
0	113	906
1	263	878
2	819	828
3	4388	824
done	5000	824

prune356.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
4.4b	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

19.0ms	(/ 1 (- a t))
78.0ms	(* (- t z) (/ 1 (- a t)))
1.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

series456.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ 1 (- a t))
89.0ms	(* (- t z) (/ 1 (- a t)))
313.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

simplify6.5s

Counts

114 → 114

Iterations

Useful iterations: done (6.5s)

Iter	Nodes	Cost
0	149	1273
1	357	1117
2	2932	942
done	5001	936

prune355.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
7.3b	(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

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:

6.0ms	(cbrt (- t z))
7.0ms	(cbrt (- t z))
8.0ms	(cbrt (- t z))
1.0ms	(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

series776.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (- t z))
168.0ms	(cbrt (- t z))
203.0ms	(cbrt (- t z))
242.0ms	(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

simplify1.1s

Counts

73 → 73

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	93	913
1	189	895
2	479	737
3	1659	666
done	5000	630

prune371.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
8.7b	(fma (* (- t z) (/ (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))) y (+ x y))

rewrite16.0ms

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:

5.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
0.0ms	(fma (* (- t z) (/ (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))) y (+ x y))

series853.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt (- a t))
219.0ms	(cbrt (- a t))
201.0ms	(cbrt (- a t))
232.0ms	(fma (* (- t z) (/ (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))) y (+ x y))

simplify934.0ms

Counts

73 → 73

Iterations

Useful iterations: done (931.0ms)

Iter	Nodes	Cost
0	95	939
1	192	921
2	483	759
3	1726	666
done	5002	630

prune442.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.0b

regimes404.0ms

Accuracy

32.7% (5.5b remaining)

Error of 8.8b against oracle of 3.3b and baseline of 11.5b

bsearch161.0ms

Steps

Iters	Range		Point
8	3.87843193862682e-153	1.975580889743198e-149	1.5571992364465793e-151
9	-1.1162846725084656e-85	-1.5650124112905035e-91	-1.459767150779762e-90

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	20	42
1	27	29
done	27	29

end0.0ms

sample1.5s

Algorithm

intervals

Results

665.0ms	7402×	body	80	valid
135.0ms	462×	body	640	valid
70.0ms	254×	body	1280	valid
62.0ms	382×	body	320	valid
27.0ms	242×	body	160	valid
5.0ms	13×	body	2560	valid