Details

sample34.0ms

Algorithm

intervals

Results

12.0ms

269×

body

valid

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	75	15
4	112	15
5	148	15
6	181	15
7	257	15
8	419	15
9	728	15
10	1525	15
11	4096	15
done	5000	15

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (- t a))
1.0b	(fma x y (* z (- t a)))
23.5b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-r`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`sub-neg` `associate-*r/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 85

Calls

3 calls:

45.0ms	(* z (- t a))
1.0ms	(fma x y (* z (- t a)))
20.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series790.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* z (- t a))
106.0ms	(fma x y (* z (- t a)))
609.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify2.5s

Counts

94 → 94

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	163	1562
1	293	1378
2	669	1188
3	2700	1146
done	5000	1092

prune401.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.8b	(/ 1 (fma z (- b y) y))
1.0b	(fma x y (* z (- t a)))
23.4b	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
18×	`associate-r` `prod-diff`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
6×	`associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `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 → 127

Calls

4 calls:

49.0ms	(* z (- t a))
12.0ms	(/ 1 (fma z (- b y) y))
1.0ms	(fma x y (* z (- t a)))
38.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* z (- t a))
112.0ms	(/ 1 (fma z (- b y) y))
90.0ms	(fma x y (* z (- t a)))
582.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

simplify3.4s

Counts

139 → 139

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	200	2133
1	387	1818
2	915	1550
3	3812	1508
done	5000	1508

prune552.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.5b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
1.0b	(fma x y (* z (- t a)))
23.6b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

49.0ms	(* z (- t a))
16.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
5.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series1.1s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* z (- t a))
759.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
58.0ms	(fma x y (* z (- t a)))
193.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify3.1s

Counts

175 → 175

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	264	3896
1	509	3507
2	1078	3118
3	4059	3058
done	5000	3058

prune675.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
0.8b	(/ 1 (fma x y (* z (- t a))))
1.0b	(fma x y (* z (- t a)))
22.9b	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`div-exp` `add-cbrt-cube`
16×	`prod-exp`
13×	`associate-r`
10×	`pow1` `rec-exp` `1-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `associate-/r/` `un-div-inv` `inv-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 123

Calls

4 calls:

33.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
6.0ms	(/ 1 (fma x y (* z (- t a))))
0.0ms	(fma x y (* z (- t a)))
20.0ms	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

800.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
138.0ms	(/ 1 (fma x y (* z (- t a))))
84.0ms	(fma x y (* z (- t a)))
229.0ms	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

simplify3.1s

Counts

135 → 135

Iterations

Useful iterations: 2 (206.0ms)

Iter	Nodes	Cost
0	147	2456
1	303	2164
2	766	1824
3	2775	1824
done	5000	1824

prune381.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 12.1b

regimes748.0ms

Accuracy

30.1% (8.4b remaining)

Error of 19.5b against oracle of 11.0b and baseline of 23.1b

bsearch86.0ms

Steps

Iters	Range		Point
8	7.200492276208318e+78	4.6647765810645656e+82	4.440792624921617e+82
7	-2.448414503336037e+180	-1.4300862413773486e+178	-1.5005152697019366e+178

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	39
1	30	33
done	30	33

end0.0ms

sample1.0s

Algorithm

intervals

Results

470.0ms

8421×

body

valid