Details

sample51.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (148.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.0b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.3b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite420.0ms

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:

28.0ms	(* (+ t y) a)
20.0ms	(+ (* (+ x y) z) (* (+ t y) a))
125.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
241.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series1.0s

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (+ t y) a)
79.0ms	(+ (* (+ x y) z) (* (+ t y) a))
140.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
778.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify1.6s

Counts

117 → 117

Iterations

Useful iterations: done (1.5s)

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

prune523.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.0b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.4b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite475.0ms

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:

39.0ms	(/ 1 (+ (+ x t) y))
16.0ms	(+ (* (+ x y) z) (* (+ t y) a))
88.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
327.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series1.1s

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ 1 (+ (+ x t) y))
72.0ms	(+ (* (+ x y) z) (* (+ t y) a))
142.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
762.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify3.5s

Counts

145 → 145

Iterations

Useful iterations: 2 (665.0ms)

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

prune597.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.5b

localize61.0ms

Local error

Found 4 expressions with local error:

5.8b	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (/ (+ (+ x t) y) (cbrt (fma z (+ x y) (fma a t (* y (- a b)))))))
26.0b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.0b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.0b	(cbrt (fma z (+ x y) (fma a t (* y (- a b)))))

rewrite363.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
94×	`times-frac`
41×	`add-sqr-sqrt` `add-cube-cbrt`
39×	`cbrt-prod`
36×	`distribute-lft-out`
34×	`associate-/r*`
16×	`add-exp-log` `cbrt-div`
10×	`add-cbrt-cube`
8×	`flip3--` `flip--` `associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `div-inv`
2×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 141

Calls

4 calls:

236.0ms	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (/ (+ (+ x t) y) (cbrt (fma z (+ x y) (fma a t (* y (- a b)))))))
55.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
61.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
1.0ms	(cbrt (fma z (+ x y) (fma a t (* y (- a b)))))

series2.7s

Counts

4 → 12

Calls

4 calls:

1.4s	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (/ (+ (+ x t) y) (cbrt (fma z (+ x y) (fma a t (* y (- a b)))))))
486.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
493.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
311.0ms	(cbrt (fma z (+ x y) (fma a t (* y (- a b)))))

simplify2.6s

Counts

153 → 153

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	225	7747
1	621	7282
2	4151	6795
done	5000	6787

prune697.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (- a b))
0.0b	(/ 1 (+ (+ x t) y))
0.5b	(fma t a (* y (- a b)))
17.5b	(* (fma t a (* y (- a b))) (/ 1 (+ (+ x t) y)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

22.0ms	(* y (- a b))
36.0ms	(/ 1 (+ (+ x t) y))
0.0ms	(fma t a (* y (- a b)))
79.0ms	(* (fma t a (* y (- a b))) (/ 1 (+ (+ x t) y)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* y (- a b))
59.0ms	(/ 1 (+ (+ x t) y))
36.0ms	(fma t a (* y (- a b)))
105.0ms	(* (fma t a (* y (- a b))) (/ 1 (+ (+ x t) y)))

simplify1.0s

Counts

157 → 157

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	209	2272
1	492	1897
2	2391	1647
done	5002	1619

prune280.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 9.5b

regimes476.0ms

Accuracy

52.5% (8.8b remaining)

Error of 17.1b against oracle of 8.3b and baseline of 26.8b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	71
1	33	71
done	33	71

end0.0ms

sample1.1s

Algorithm

intervals

Results

657.0ms	7997×	body	80	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid