Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	225×	body	80	valid
4.0ms	25×	body	640	valid
2.0ms	10×	body	1280	valid
1.0ms	11×	body	320	valid
1.0ms	5×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	3757
7	2046
6	989
5	406
4	195
3	103
2	50
1	22
0	11

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.2b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
13.0b	(fma (- t z) (/ y (- a t)) (+ x y))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `fma-udef` `div-inv` `flip--`

Counts

2 → 51

Calls

2 calls:

12.0ms	(/ y (- a t))
0.0ms	(fma (- t z) (/ y (- a t)) (+ x y))

series214.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ y (- a t))
159.0ms	(fma (- t z) (/ y (- a t)) (+ x y))

simplify1.2s

Counts

57 → 57

Iterations

Iter	Nodes
done	5000
3	1386
2	456
1	176
0	94

prune385.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
2.9b	(+ (* (- t z) (/ y (- a t))) (+ x y))
9.1b	(* (- t z) (/ y (- a t)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-cbrt-cube` `frac-add` `add-exp-log`
8×	`flip3--` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
5×	`pow1` `associate-/r` `associate-l*`
4×	`associate-/r/`
3×	`expm1-log1p-u` `sum-log` `associate-r/` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `clear-num` `fma-def` `frac-2neg` `pow-prod-down` `*-commutative`

Counts

3 → 116

Calls

3 calls:

20.0ms	(/ y (- a t))
64.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
68.0ms	(* (- t z) (/ y (- a t)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ y (- a t))
190.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
90.0ms	(* (- t z) (/ y (- a t)))

simplify2.4s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	3040
1	675
0	217

prune893.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.9b	(* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t)))))
10.5b	(+ (* (* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

rewrite699.0ms

Algorithm

rewrite-expression-head

Rules

67×	`frac-times`
47×	`associate-*l/`
46×	`frac-add`
32×	`associate-*r/`
24×	`flip3-+` `flip-+`
22×	`flip3--` `add-exp-log` `flip--`
14×	`add-sqr-sqrt` `add-cbrt-cube`
13×	`*-un-lft-identity`
10×	`cbrt-prod`
9×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
7×	`add-cube-cbrt`
5×	`associate-l`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-div` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`+-commutative` `associate-+r+` `fma-def` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

4.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
173.0ms	(* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t)))))
512.0ms	(+ (* (* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

series1.2s

Counts

4 → 12

Calls

4 calls:

220.0ms	(cbrt (- a t))
192.0ms	(cbrt (- a t))
430.0ms	(* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t)))))
314.0ms	(+ (* (* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

simplify2.2s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
1	1423
0	417

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.9b

localize101.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
0.6b	(cbrt (cbrt (- a t)))
2.9b	(* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t)))))
9.5b	(+ (* (* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t))))) (/ (cbrt y) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (+ x y))

rewrite734.0ms

Algorithm

rewrite-expression-head

Rules

71×	`frac-times`
49×	`associate-*l/`
46×	`frac-add`
34×	`associate-*r/`
27×	`flip3--` `flip--`
24×	`cbrt-div` `flip3-+` `flip-+`
22×	`add-exp-log`
14×	`cbrt-prod` `add-cbrt-cube`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
7×	`add-cube-cbrt`
5×	`associate-l`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `pow-prod-down`
2×	`pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `fma-def` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

28.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
9.0ms	(cbrt (cbrt (- a t)))
145.0ms	(* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t)))))
542.0ms	(+ (* (* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t))))) (/ (cbrt y) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (+ x y))

series1.1s

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
247.0ms	(cbrt (cbrt (- a t)))
387.0ms	(* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t)))))
271.0ms	(+ (* (* (- t z) (* (/ (cbrt y) (cbrt (- a t))) (/ (cbrt y) (cbrt (- a t))))) (/ (cbrt y) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (+ x y))

simplify3.4s

Counts

157 → 157

Iterations

Iter	Nodes
done	5001
1	1677
0	510

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.9b

regimes993.0ms

Accuracy

43.9% (4.3b remaining)

Error of 7.6b against oracle of 3.3b and baseline of 11.0b

bsearch112.0ms

Steps

Iters	Range		Point
7	2.529877801601859e+142	1.2575529428174224e+144	3.963652201301505e+142
5	-2.3191845918248765e+129	-1.00089535068003e+129	-1.8666316459197392e+129

simplify13.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s	7267×	body	80	valid
160.0ms	484×	body	640	valid
109.0ms	380×	body	320	valid
87.0ms	278×	body	1280	valid
33.0ms	249×	body	160	valid
3.0ms	9×	body	2560	valid