Details

sample77.0ms

Algorithm

intervals

Results

37.0ms

275×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	1738
8	588
7	279
6	203
5	170
4	125
3	75
2	43
1	24
0	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
1.7b	(+ (* x y) (* z (- t a)))
26.3b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 161

Calls

4 calls:

18.0ms	(* z (- t a))
24.0ms	(* z (- b y))
20.0ms	(+ (* x y) (* z (- t a)))
55.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series712.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* z (- t a))
58.0ms	(* z (- b y))
86.0ms	(+ (* x y) (* z (- t a)))
510.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify1.7s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	2874
1	710
0	291

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 26.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.5b	(/ 1 (fma z (- b y) y))
1.7b	(+ (* x y) (* z (- t a)))
25.8b	(* (+ (* x y) (* z (- t a))) (/ 1 (fma z (- b y) y)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 157

Calls

4 calls:

31.0ms	(* z (- t a))
8.0ms	(/ 1 (fma z (- b y) y))
20.0ms	(+ (* x y) (* z (- t a)))
58.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma z (- b y) y)))

series806.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* z (- t a))
88.0ms	(/ 1 (fma z (- b y) y))
99.0ms	(+ (* x y) (* z (- t a)))
538.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma z (- b y) y)))

simplify2.7s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	3265
1	579
0	237

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 26.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.4b	(/ 1 (/ (fma z (- b y) y) (fma z (- t a) (* y x))))
1.0b	(fma z (- t a) (* y x))
26.4b	(/ (fma z (- b y) y) (fma z (- t a) (* y x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma z (- b y) y)
9.0ms	(/ 1 (/ (fma z (- b y) y) (fma z (- t a) (* y x))))
0.0ms	(fma z (- t a) (* y x))
4.0ms	(/ (fma z (- b y) y) (fma z (- t a) (* y x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma z (- b y) y)
854.0ms	(/ 1 (/ (fma z (- b y) y) (fma z (- t a) (* y x))))
56.0ms	(fma z (- t a) (* y x))
172.0ms	(/ (fma z (- b y) y) (fma z (- t a) (* y x)))

simplify1.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	5002
2	1650
1	401
0	179

prune898.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 17.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
1.7b	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- t a))))
26.3b	(/ (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- t a)))) (+ y (* z (- b y))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

44×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
38×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
36×	`prod-diff`
9×	`times-frac`
6×	`cbrt-prod` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `log1p-expm1-u`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 117

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
34.0ms	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- t a))))
34.0ms	(/ (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- t a)))) (+ y (* z (- b y))))

series1.6s

Counts

4 → 12

Calls

4 calls:

295.0ms	(cbrt z)
371.0ms	(cbrt z)
215.0ms	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- t a))))
699.0ms	(/ (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- t a)))) (+ y (* z (- b y))))

simplify2.6s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	3224
1	718
0	240

prune982.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 17.4b

regimes1.3s

Accuracy

43.9% (4.7b remaining)

Error of 19.6b against oracle of 14.9b and baseline of 23.2b

bsearch163.0ms

Steps

Iters	Range		Point
11	7.688672617548883e+59	1.8652761479291097e+80	3.9544459558456954e+76
8	-2.0700515967326768e+49	-3.6339803350820565e+44	-2.034080329997318e+49

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s

8413×

body

valid