Details

sample45.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (145.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (- z b))
0.8b	(fma x z (* y (- z b)))
2.0b	(fma a (+ t y) (fma x z (* y (- z b))))
21.7b	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

rewrite69.0ms

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:

29.0ms	(* y (- z b))
0.0ms	(fma x z (* y (- z b)))
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))

series847.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* y (- z b))
60.0ms	(fma x z (* y (- z b)))
156.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
563.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

simplify1.7s

Counts

117 → 117

Iterations

Useful iterations: 3 (706.0ms)

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

prune389.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma a (+ t y) (fma x z (* y (- z b))))))
0.8b	(fma x z (* y (- z b)))
2.0b	(fma a (+ t y) (fma x z (* y (- z b))))
21.7b	(/ (+ (+ x t) y) (fma a (+ t y) (fma x z (* y (- z b)))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
132×	`times-frac`
70×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef` `associate-/l/`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 161

Calls

4 calls:

64.0ms	(/ 1 (/ (+ (+ x t) y) (fma a (+ t y) (fma x z (* y (- z b))))))
0.0ms	(fma x z (* y (- z b)))
0.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
118.0ms	(/ (+ (+ x t) y) (fma a (+ t y) (fma x z (* y (- z b)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

820.0ms	(/ 1 (/ (+ (+ x t) y) (fma a (+ t y) (fma x z (* y (- z b))))))
52.0ms	(fma x z (* y (- z b)))
148.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
173.0ms	(/ (+ (+ x t) y) (fma a (+ t y) (fma x z (* y (- z b)))))

simplify2.5s

Counts

173 → 173

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	189	5188
1	406	4825
2	1038	4452
3	4610	4420
done	5000	4420

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
0.8b	(fma x z (* y (- z b)))
2.0b	(fma a (+ t y) (fma x z (* y (- z b))))
21.8b	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

rewrite165.0ms

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:

37.0ms	(/ 1 (+ (+ x t) y))
0.0ms	(fma x z (* y (- z b)))
0.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
123.0ms	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1 (+ (+ x t) y))
50.0ms	(fma x z (* y (- z b)))
120.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
607.0ms	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

simplify1.7s

Counts

121 → 121

Iterations

Useful iterations: 2 (123.0ms)

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

prune314.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma x z (* y (- z b)))
0.8b	(/ 1 (fma a (+ t y) (fma x z (* y (- z b)))))
2.0b	(fma a (+ t y) (fma x z (* y (- z b))))
21.0b	(/ (/ 1 (+ (+ x t) y)) (/ 1 (fma a (+ t y) (fma x z (* y (- z b))))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

690×	`times-frac`
502×	`*-un-lft-identity`
292×	`add-sqr-sqrt` `add-cube-cbrt`
126×	`distribute-lft-out`
48×	`add-exp-log`
38×	`div-inv`
34×	`div-exp`
29×	`associate-/r/`
24×	`associate-/l*`
18×	`add-cbrt-cube`
16×	`associate-/r*`
14×	`flip3-+` `flip-+`
9×	`cbrt-undiv` `rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

4 → 394

Calls

4 calls:

0.0ms	(fma x z (* y (- z b)))
6.0ms	(/ 1 (fma a (+ t y) (fma x z (* y (- z b)))))
0.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
72.0ms	(/ (/ 1 (+ (+ x t) y)) (/ 1 (fma a (+ t y) (fma x z (* y (- z b))))))

series893.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma x z (* y (- z b)))
78.0ms	(/ 1 (fma a (+ t y) (fma x z (* y (- z b)))))
121.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
652.0ms	(/ (/ 1 (+ (+ x t) y)) (/ 1 (fma a (+ t y) (fma x z (* y (- z b))))))

simplify1.2s

Counts

406 → 406

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	479	16935
1	1327	14505
2	2559	13547
done	5001	13439

prune483.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.4b

regimes544.0ms

Accuracy

46.5% (11.8b remaining)

Error of 16.0b against oracle of 4.3b and baseline of 26.3b

bsearch112.0ms

Steps

Iters	Range		Point
10	1.848926544553742e+57	2.10145004435701e+68	1.4432684579839212e+66
9	-5.4816814859009735e+150	-1.3880569002884752e+141	-1.4117648173565642e+141

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	37
1	30	33
done	30	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

685.0ms	7999×	body	80	valid
0.0ms	1×	body	160	valid