Details

sample63.0ms

Algorithm

intervals

Results

18.0ms	234×	body	80	valid
6.0ms	20×	body	640	valid
3.0ms	8×	body	1280	valid
3.0ms	13×	body	320	valid
1.0ms	7×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (67.0ms)

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.1b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite44.0ms

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:

40.0ms	(/ (- t z) (- a t))
1.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series326.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ (- t z) (- a t))
255.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.6s

Counts

70 → 70

Iterations

Useful iterations: 3 (922.0ms)

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

prune289.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
8.2b	(fma (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) y (+ x y))

rewrite28.0ms

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:

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

series915.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(cbrt (- a t))
206.0ms	(cbrt (- a t))
221.0ms	(cbrt (- a t))
294.0ms	(fma (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) y (+ x y))

simplify1.3s

Counts

73 → 73

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	93	913
1	191	895
2	474	737
3	1585	666
done	5000	630

prune460.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- a t)))
0.6b	(cbrt (cbrt (- a t)))
0.6b	(cbrt (cbrt (- a t)))
11.4b	(fma (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (cbrt (cbrt (- a t))))) y (+ x y))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
16×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`cbrt-div`
10×	`add-cube-cbrt`
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 → 70

Calls

4 calls:

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

series854.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (cbrt (- a t)))
211.0ms	(cbrt (cbrt (- a t)))
203.0ms	(cbrt (cbrt (- a t)))
281.0ms	(fma (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (cbrt (cbrt (- a t))))) y (+ x y))

simplify1.0s

Counts

82 → 82

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	108	1271
1	209	1244
2	517	1032
3	1857	967
done	5002	846

prune587.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t z))
0.6b	(cbrt (- t z))
0.6b	(cbrt (- t z))
8.7b	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y (+ x y))

rewrite31.0ms

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:

7.0ms	(cbrt (- t z))
7.0ms	(cbrt (- t z))
14.0ms	(cbrt (- t z))
1.0ms	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y (+ x y))

series927.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt (- t z))
231.0ms	(cbrt (- t z))
214.0ms	(cbrt (- t z))
266.0ms	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y (+ x y))

simplify1.0s

Counts

73 → 73

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	93	913
1	192	895
2	480	737
3	1653	666
done	5000	630

prune293.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.9b

regimes350.0ms

Accuracy

39.9% (4.8b remaining)

Error of 8.2b against oracle of 3.4b and baseline of 11.3b

bsearch102.0ms

Steps

Iters	Range		Point
4	4.536853709009945e+119	8.134383085006714e+119	7.272461153412324e+119
10	-2.7976687006233133e+82	-3.132629721821513e+67	-1.2188467661632975e+82

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	18	32
1	22	27
done	22	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

588.0ms	7376×	body	80	valid
89.0ms	458×	body	640	valid
84.0ms	257×	body	1280	valid
54.0ms	377×	body	320	valid
48.0ms	230×	body	160	valid
6.0ms	22×	body	2560	valid