Details

sample59.0ms

Algorithm

intervals

Results

28.0ms

256×

body

valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (138.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	79	20
3	201	20
4	637	19
5	2240	19
6	4952	19
done	5000	19

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.2b	(+ (* (+ x y) z) (* (+ t y) a))
1.3b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.7b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

30.0ms	(* (+ t y) a)
25.0ms	(+ (* (+ x y) z) (* (+ t y) a))
127.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
240.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series1.0s

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (+ t y) a)
79.0ms	(+ (* (+ x y) z) (* (+ t y) a))
142.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
756.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify1.8s

Counts

117 → 117

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	192	2540
1	574	2315
2	2559	2104
done	5002	2080

prune802.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.2b	(+ (* (+ x y) z) (* (+ t y) a))
1.3b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.7b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

38.0ms	(/ 1 (+ (+ x t) y))
21.0ms	(+ (* (+ x y) z) (* (+ t y) a))
100.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
379.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series1.2s

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ 1 (+ (+ x t) y))
74.0ms	(+ (* (+ x y) z) (* (+ t y) a))
166.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
828.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify3.6s

Counts

145 → 145

Iterations

Useful iterations: 2 (787.0ms)

Iter	Nodes	Cost
0	207	2953
1	626	2602
2	4267	2274
done	5000	2274

prune763.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.4b

localize54.0ms

Local error

Found 4 expressions with local error:

1.8b	(fma z (+ x y) (fma t a (* y (- a b))))
24.7b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
24.7b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
24.7b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

rewrite185.0ms

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 z (+ x y) (fma t a (* y (- a b))))
55.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
55.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
68.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

series1.6s

Counts

4 → 12

Calls

4 calls:

120.0ms	(fma z (+ x y) (fma t a (* y (- a b))))
506.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
501.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
493.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

simplify1.4s

Counts

139 → 139

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	81	3706
1	178	3627
2	526	3371
3	2450	3371
done	5000	3371

prune723.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.4b

localize52.0ms

Local error

Found 4 expressions with local error:

6.7b	(/ (/ (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (cbrt (+ (+ x t) y)))
17.9b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
24.7b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
24.7b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

196×	`*-un-lft-identity`
180×	`times-frac`
122×	`cbrt-div`
86×	`associate-/r/`
80×	`cbrt-prod`
76×	`add-sqr-sqrt` `add-cube-cbrt`
72×	`distribute-lft-out`
63×	`flip3-+` `flip-+`
40×	`frac-times`
24×	`associate-/l*`
22×	`add-exp-log`
20×	`associate-r/` `associate-l/`
19×	`associate-/r*`
15×	`add-cbrt-cube`
13×	`div-inv`
9×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 273

Calls

4 calls:

97.0ms	(/ (/ (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (cbrt (+ (+ x t) y)))
47.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
38.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
36.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

series3.6s

Counts

4 → 12

Calls

4 calls:

484.0ms	(/ (/ (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (cbrt (+ (+ x t) y)))
2.2s	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
458.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
460.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

simplify1.2s

Counts

285 → 285

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	350	12964
1	841	12206
2	3469	11653
done	5000	11618

prune1.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 8.4b

regimes661.0ms

Accuracy

18.2% (14.5b remaining)

Error of 23.0b against oracle of 8.5b and baseline of 26.2b

bsearch41.0ms

Steps

Iters	Range		Point
0	5.391138130598216e+163	5.558519705629081e+163	5.4748289181136484e+163
7	-3.772982779093367e+114	-9.211061856865476e+112	-1.4182932798752201e+113

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	33
1	38	33
done	38	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

699.0ms	7995×	body	80	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid