Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (49.0ms)

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	2125	19
8	4017	19
done	5001	19

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.6b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
1.8b	(+ (* (+ x y) z) (* (+ t y) a))
23.3b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite150.0ms

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	(* (+ t y) a)
41.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
89.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series853.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ t y) a)
108.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
58.0ms	(+ (* (+ x y) z) (* (+ t y) a))
664.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify757.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (227.0ms)

Iter	Nodes	Cost
0	192	2540
1	564	2315
2	2161	2102
done	5000	2102

prune706.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.6b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
1.8b	(+ (* (+ x y) z) (* (+ t y) a))
23.4b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

11.0ms	(* (+ t y) a)
43.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
145.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series841.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (+ t y) a)
110.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
52.0ms	(+ (* (+ x y) z) (* (+ t y) a))
657.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify919.0ms

Counts

125 → 125

Iterations

Useful iterations: 2 (308.0ms)

Iter	Nodes	Cost
0	219	2652
1	646	2314
2	2459	2043
done	5000	2043

prune459.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
1.6b	(- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b))
1.8b	(+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a)))
23.3b	(/ (- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b)) (+ (+ x t) y))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
12×	`associate-*l/` `distribute-lft-out`
11×	`add-log-exp`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`cbrt-prod` `fma-neg` `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` `pow1/3` `div-sub` `div-exp` `associate--l+` `clear-num` `div-inv`

Counts

4 → 95

Calls

4 calls:

1.0ms	(cbrt a)
50.0ms	(- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b))
9.0ms	(+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a)))
96.0ms	(/ (- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b)) (+ (+ x t) y))

series1.2s

Counts

4 → 12

Calls

4 calls:

195.0ms	(cbrt a)
180.0ms	(- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b))
113.0ms	(+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a)))
743.0ms	(/ (- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b)) (+ (+ x t) y))

simplify721.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (234.0ms)

Iter	Nodes	Cost
0	193	3226
1	565	2993
2	2120	1997
done	5000	1997

prune402.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize25.0ms

Local error

Found 4 expressions with local error:

2.8b	(fma z (+ x y) (fma t a (* y (- a b))))
23.3b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
23.3b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
23.3b	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

rewrite61.0ms

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))))
19.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
19.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
19.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

series1.5s

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma z (+ x y) (fma t a (* y (- a b))))
451.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
449.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))
449.0ms	(/ (fma z (+ x y) (fma t a (* y (- a b)))) (+ (+ x t) y))

simplify828.0ms

Counts

139 → 139

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	81	3706
1	177	3627
2	467	3371
3	1663	3371
done	5002	3371

prune513.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.6b

regimes476.0ms

Accuracy

15.2% (14.9b remaining)

Error of 23.4b against oracle of 8.5b and baseline of 26.1b

bsearch222.0ms

Steps

Iters	Range		Point
8	9.688319091200168e+210	4.7471826758723055e+213	2.7492352456446427e+212
9	-1.65136639351713e-266	-7.451480749479347e-273	-1.6194793515167915e-266
8	-6.170392859290159e-228	-2.0779468591431954e-230	-2.1108017491855503e-230
8	-8.278918965766029e+130	-2.283374321947351e+128	-2.0102242405280762e+130

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	65
1	41	65
done	41	65

end0.0ms

sample636.0ms

Algorithm

intervals

Results

373.0ms	7998×	body	80	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid