Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify6.5s

Counts

1 → 1

Iterations

Useful iterations: 4 (57.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	78	20
3	152	20
4	367	19
5	682	19
6	1142	19
7	2136	19
8	4079	19
done	5000	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.6b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
1.9b	(+ (* (+ x y) z) (* (+ t y) a))
26.7b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite140.0ms

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:

10.0ms	(* (+ x y) z)
39.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
82.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series781.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ x y) z)
99.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
50.0ms	(+ (* (+ x y) z) (* (+ t y) a))
610.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify760.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (233.0ms)

Iter	Nodes	Cost
0	194	2540
1	569	2317
2	2166	2102
done	5001	2102

prune409.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
0.3b	(fma a t (* y (- a b)))
0.8b	(fma z (+ x y) (fma a t (* y (- a b))))
26.7b	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

rewrite63.0ms

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:

21.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
0.0ms	(fma a t (* y (- a b)))
0.0ms	(fma z (+ x y) (fma a t (* y (- a b))))
35.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

series836.0ms

Counts

4 → 12

Calls

4 calls:

585.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
34.0ms	(fma a t (* y (- a b)))
103.0ms	(fma z (+ x y) (fma a t (* y (- a b))))
114.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

simplify2.2s

Counts

173 → 173

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	190	5188
1	423	4897
2	1153	4452
3	4503	4420
done	5001	4420

prune377.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.9b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify4.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune26.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (- a b))
0.3b	(fma a t (* y (- a b)))
0.8b	(fma (+ x y) z (fma a t (* y (- a b))))
26.7b	(/ (fma (+ x y) z (fma a t (* y (- a b)))) (+ (+ x t) y))

rewrite35.0ms

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:

14.0ms	(* y (- a b))
0.0ms	(fma a t (* y (- a b)))
0.0ms	(fma (+ x y) z (fma a t (* y (- a b))))
17.0ms	(/ (fma (+ x y) z (fma a t (* y (- a b)))) (+ (+ x t) y))

series446.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* y (- a b))
33.0ms	(fma a t (* y (- a b)))
100.0ms	(fma (+ x y) z (fma a t (* y (- a b))))
275.0ms	(/ (fma (+ x y) z (fma a t (* y (- a b)))) (+ (+ x t) y))

simplify1.4s

Counts

117 → 117

Iterations

Useful iterations: 3 (481.0ms)

Iter	Nodes	Cost
0	183	2221
1	347	2023
2	871	1783
3	3153	1741
done	5000	1741

prune280.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.9b

regimes527.0ms

Accuracy

51.2% (11.7b remaining)

Error of 16.4b against oracle of 4.7b and baseline of 28.7b

bsearch58.0ms

Steps

Iters	Range		Point
3	7.737347823732857e+99	9.606492792420655e+99	7.827372825110575e+99
8	-1.0974072141907462e+120	-2.9310234072330656e+117	-3.057173118340997e+117

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	24	39
1	35	33
done	35	33

end0.0ms

sample616.0ms

Algorithm

intervals

Results

356.0ms	7999×	body	80	valid
0.0ms	1×	body	160	valid