Details

sample41.0ms

Algorithm

intervals

Results

14.0ms	237×	body	80	valid
4.0ms	16×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	4×	body	2560	valid
1.0ms	11×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
6	2502
5	895
4	343
3	126
2	46
1	23
0	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.0b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.1b	(* (- y z) (/ (- t x) (- a z)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 131

Calls

3 calls:

32.0ms	(/ (- t x) (- a z))
10.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
76.0ms	(* (- y z) (/ (- t x) (- a z)))

series519.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (- t x) (- a z))
214.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
217.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.9s

Counts

140 → 140

Iterations

Iter	Nodes
done	5006
2	1822
1	518
0	192

prune759.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t x))
0.5b	(* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))
0.9b	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
9.8b	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

485×	`cbrt-prod`
426×	`*-un-lft-identity`
396×	`add-sqr-sqrt`
373×	`times-frac`
156×	`add-cube-cbrt`
115×	`distribute-lft-out--`
106×	`swap-sqr`
75×	`difference-of-squares`
70×	`associate-r` `associate-l`
34×	`add-exp-log`
25×	`unswap-sqr`
18×	`add-cbrt-cube`
13×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/r/`
10×	`cbrt-div`
8×	`prod-exp` `cbrt-unprod`
6×	`flip3--` `flip--` `add-log-exp`
5×	`div-inv` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-times` `associate-l/` `associate-r/` `associate-/l/`
1×	`pow2` `+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `flip3-+` `pow-plus` `pow1/3` `div-sub` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `flip-+`

Counts

4 → 373

Calls

4 calls:

5.0ms	(cbrt (- t x))
211.0ms	(* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))
63.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
7.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (- t x))
258.0ms	(* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))
517.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
210.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify3.5s

Counts

385 → 385

Iterations

Iter	Nodes
done	5000
2	4917
1	1748
0	525

prune2.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.7b

localize85.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.9b	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
13.1b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

2.0ms	(cbrt x)
1.0ms	(cbrt x)
96.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

334.0ms	(cbrt x)
273.0ms	(cbrt x)
593.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
269.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify2.3s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1156
1	410
0	168

prune774.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
1.3b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
13.2b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-div`
35×	`add-sqr-sqrt`
31×	`cbrt-prod` `*-un-lft-identity`
27×	`add-exp-log`
25×	`associate-l`
24×	`frac-times` `flip3--` `flip--`
16×	`pow1` `associate-*r/`
15×	`add-cbrt-cube` `add-cube-cbrt`
12×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr`
9×	`associate-r` `associate-*l/`
8×	`associate-/r/`
7×	`pow1/3` `distribute-lft-out--`
6×	`times-frac` `unswap-sqr`
5×	`pow-prod-down` `difference-of-squares`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus` `fma-udef` `div-inv`

Counts

4 → 146

Calls

4 calls:

1.0ms	(cbrt x)
69.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
204.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

227.0ms	(cbrt x)
144.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
621.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
182.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify2.0s

Counts

158 → 158

Iterations

Iter	Nodes
done	5008
2	2297
1	746
0	301

prune1.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 5.7b

regimes995.0ms

Accuracy

1.6% (8.8b remaining)

Error of 12.4b against oracle of 3.5b and baseline of 12.5b

bsearch162.0ms

Steps

Iters	Range		Point
7	169856284.9237695	13400677057.571825	13189468142.046627
8	-3.7025101036668716e+145	-5.475978031765872e+141	-8.629542751842365e+143

simplify13.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	7798×	body	80	valid
204.0ms	509×	body	640	valid
128.0ms	373×	body	320	valid
81.0ms	274×	body	1280	valid
31.0ms	279×	body	160	valid
3.0ms	10×	body	2560	valid