Details

sample60.0ms

Algorithm

intervals

Results

35.0ms

256×

body

valid

simplify7.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (111.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	79	20
3	201	20
4	405	19
5	766	19
6	1278	19
7	2257	19
8	4193	19
done	5000	19

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (- z b))
1.5b	(fma x z (* y (- z b)))
2.0b	(fma a (+ t y) (fma x z (* y (- z b))))
26.8b	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
18×	`prod-diff`
15×	`times-frac`
12×	`distribute-lft-out`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`associate-r` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/l*`
2×	`sub-neg` `associate-*r/` `associate-/r/` `fma-udef`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

38.0ms	(* y (- z b))
0.0ms	(fma x z (* y (- z b)))
0.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
44.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

series754.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* y (- z b))
45.0ms	(fma x z (* y (- z b)))
137.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
521.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

simplify1.8s

Counts

117 → 117

Iterations

Useful iterations: 3 (772.0ms)

Iter	Nodes	Cost
0	182	2221
1	353	2023
2	892	1783
3	3630	1741
done	5000	1741

prune390.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.5b	(fma x z (* y (- z b)))
2.0b	(fma a (+ t y) (fma x z (* y (- z b))))
26.9b	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 109

Calls

4 calls:

45.0ms	(/ 1 (+ (+ x t) y))
0.0ms	(fma x z (* y (- z b)))
0.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
109.0ms	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

series848.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1 (+ (+ x t) y))
47.0ms	(fma x z (* y (- z b)))
144.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
581.0ms	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

simplify2.1s

Counts

121 → 121

Iterations

Useful iterations: 2 (174.0ms)

Iter	Nodes	Cost
0	129	2017
1	287	1805
2	823	1597
3	3622	1597
done	5000	1597

prune423.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.3b

localize50.0ms

Local error

Found 4 expressions with local error:

1.5b	(fma x z (* y (- z b)))
2.0b	(fma a (+ t y) (fma x z (* y (- z b))))
12.4b	(* (/ (fma a (+ t y) (fma x z (* y (- z b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ (sqrt 1) (cbrt (+ (+ x t) y))))
14.3b	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt` `times-frac`
71×	`*-un-lft-identity`
54×	`associate-r`
37×	`add-cube-cbrt`
36×	`cbrt-prod`
32×	`sqrt-prod`
30×	`add-exp-log`
26×	`cbrt-div`
21×	`add-cbrt-cube`
18×	`associate-/r/` `distribute-lft-out`
15×	`associate-l`
14×	`unswap-sqr`
13×	`flip3-+` `flip-+`
9×	`cbrt-undiv` `frac-times` `div-exp` `prod-exp` `cbrt-unprod`
6×	`pow1`
5×	`associate-r/` `associate-l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`fma-udef`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative`

Counts

4 → 160

Calls

4 calls:

0.0ms	(fma x z (* y (- z b)))
1.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
352.0ms	(* (/ (fma a (+ t y) (fma x z (* y (- z b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ (sqrt 1) (cbrt (+ (+ x t) y))))
88.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

series3.4s

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma x z (* y (- z b)))
159.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
579.0ms	(* (/ (fma a (+ t y) (fma x z (* y (- z b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ (sqrt 1) (cbrt (+ (+ x t) y))))
2.6s	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

simplify1.2s

Counts

172 → 172

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	291	6534
1	798	6005
2	2130	5073
done	5001	4921

prune593.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 9.2b

localize27.0ms

Local error

Found 4 expressions with local error:

2.0b	(fma a (+ t y) (fma x z (* y (- z b))))
26.8b	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))
26.8b	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))
26.8b	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

94×	`*-un-lft-identity`
45×	`times-frac`
36×	`distribute-lft-out`
34×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
35.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))
34.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))
40.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

series1.5s

Counts

4 → 12

Calls

4 calls:

119.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
461.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))
460.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))
458.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

simplify1.1s

Counts

139 → 139

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	81	3706
1	175	3629
2	507	3371
3	1983	3371
done	5000	3371

prune477.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 9.2b

regimes495.0ms

Accuracy

14% (15.6b remaining)

Error of 23.9b against oracle of 8.2b and baseline of 26.4b

bsearch182.0ms

Steps

Iters	Range		Point
7	1.1325161296267603e+166	2.2898271484234143e+168	1.5154820646647913e+167
9	-1.321348346219407e-13	-1.330625894769849e-19	-1.2992160673987935e-13
9	-3.6878446319725823e+46	-7.918529426048614e+40	-7.998482695214573e+40
5	-3.284918449488842e+213	-1.044051476258928e+213	-1.0616104282418916e+213

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	57
1	30	57
done	30	57

end0.0ms

sample985.0ms

Algorithm

intervals

Results

697.0ms	7997×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid