Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	238×	body	80	valid
4.0ms	14×	body	640	valid
4.0ms	10×	body	1280	valid
3.0ms	17×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	2560	valid

simplify13.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (61.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	109	13
4	203	12
5	451	12
6	748	12
7	1078	12
8	1400	12
9	1655	12
10	2153	12
11	2683	12
12	3847	12
done	5001	12

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.7b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite29.0ms

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

series403.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (- t z) (- a t))
321.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.7s

Counts

70 → 70

Iterations

Useful iterations: 3 (528.0ms)

Iter	Nodes	Cost
0	113	906
1	258	878
2	622	826
3	1643	824
done	5000	824

prune319.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
9.3b	(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

rewrite20.0ms

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 (- t z))
5.0ms	(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))

series1.1s

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt (- t z))
321.0ms	(cbrt (- t z))
216.0ms	(cbrt (- t z))
283.0ms	(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

simplify3.1s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	93	913
1	189	895
2	401	737
3	1051	666
4	4073	630
done	5000	630

prune382.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (fma y (/ (- t z) (- a t)) (+ x y)))
1.7b	(fma y (/ (- t z) (- a t)) (+ x y))
1.7b	(fma y (/ (- t z) (- a t)) (+ x y))
1.7b	(fma y (/ (- t z) (- a t)) (+ x y))

rewrite3.0ms

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:

1.0ms	(cbrt (fma y (/ (- t z) (- a t)) (+ x y)))
0.0ms	(fma y (/ (- t z) (- a t)) (+ x y))
0.0ms	(fma y (/ (- t z) (- a t)) (+ x y))
0.0ms	(fma y (/ (- t z) (- a t)) (+ x y))

series1.9s

Counts

4 → 12

Calls

4 calls:

1.4s	(cbrt (fma y (/ (- t z) (- a t)) (+ x y)))
177.0ms	(fma y (/ (- t z) (- a t)) (+ x y))
189.0ms	(fma y (/ (- t z) (- a t)) (+ x y))
195.0ms	(fma y (/ (- t z) (- a t)) (+ x y))

simplify1.3s

Counts

55 → 55

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	76	865
1	162	858
2	406	758
3	1300	744
done	5000	731

prune328.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.4b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.9b	(/ (* (- z t) y) (- a t))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
44×	`prod-diff`
27×	`add-cube-cbrt`
25×	`times-frac`
13×	`distribute-lft-out`
10×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
9×	`distribute-lft-out--`
8×	`flip3--` `flip--` `add-log-exp` `difference-of-squares`
5×	`pow1` `associate-l` `associate-/r*` `div-inv`
4×	`fma-neg` `associate-*l/`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `frac-sub` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `-commutative` `flip-+` `associate-/l` `unswap-sqr`

Counts

3 → 124

Calls

3 calls:

38.0ms	(* (- z t) y)
109.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
42.0ms	(/ (* (- z t) y) (- a t))

series365.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* (- z t) y)
206.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
116.0ms	(/ (* (- z t) y) (- a t))

simplify2.0s

Counts

133 → 133

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	231	3853
1	598	3294
2	2291	2631
done	5001	2185

prune415.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.2b

regimes396.0ms

Accuracy

27.2% (6.1b remaining)

Error of 9.3b against oracle of 3.2b and baseline of 11.6b

bsearch110.0ms

Steps

Iters	Range		Point
5	6.0100183000681985e-12	1.507024095617085e-11	6.088666730586291e-12
8	-3.918365209681127e-34	-6.813482838924963e-38	-6.928903510917508e-38

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	38
1	22	27
done	22	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

673.0ms	7381×	body	80	valid
134.0ms	458×	body	640	valid
69.0ms	257×	body	1280	valid
65.0ms	409×	body	320	valid
27.0ms	250×	body	160	valid
5.0ms	13×	body	2560	valid