Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

264×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	23	17
2	37	17
3	55	17
4	72	17
5	84	17
6	108	17
7	177	17
8	326	17
9	605	17
10	1389	17
11	3382	17
done	5001	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(+ y (* z (- b y)))
1.3b	(+ (* x y) (* z (- t a)))
25.9b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-exp-log` `associate-+r+` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `distribute-rgt-in` `sub-neg` `distribute-lft-in`
5×	`associate-r`
4×	`flip3-+` `flip-+`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`+-commutative` `associate-*r/` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

10.0ms	(* z (- b y))
3.0ms	(+ y (* z (- b y)))
3.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* z (- b y))
30.0ms	(+ y (* z (- b y)))
40.0ms	(+ (* x y) (* z (- t a)))
303.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify1.5s

Counts

99 → 99

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	146	1497
1	351	1447
2	1071	1327
3	4345	1327
done	5000	1327

prune283.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 26.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.2b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.3b	(+ (* x y) (* z (- t a)))
26.0b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`associate-+r+` `flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 145

Calls

4 calls:

3.0ms	(+ y (* z (- b y)))
10.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
3.0ms	(+ (* x y) (* z (- t a)))
13.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.1s

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ y (* z (- b y)))
796.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
39.0ms	(+ (* x y) (* z (- t a)))
253.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify546.0ms

Counts

157 → 157

Iterations

Useful iterations: 2 (179.0ms)

Iter	Nodes	Cost
0	216	4144
1	526	3878
2	1381	3553
done	5000	3553

prune357.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 26.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a)))))
0.8b	(+ (+ (* z b) y) (* z (- y)))
1.3b	(+ (* x y) (* z (- t a)))
26.0b	(/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube` `add-log-exp`
8×	`flip3-+` `div-exp` `flip-+`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `associate-+r+` `sum-log` `distribute-rgt-neg-out`
2×	`+-commutative` `distribute-rgt-in` `sub-neg` `rec-exp` `frac-2neg` `distribute-lft-in` `1-exp` `div-sub` `unsub-neg` `clear-num` `associate-/l/`
1×	`associate-+l+` `pow-flip` `inv-pow`

Counts

4 → 147

Calls

4 calls:

23.0ms	(/ 1 (/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a)))))
14.0ms	(+ (+ (* z b) y) (* z (- y)))
3.0ms	(+ (* x y) (* z (- t a)))
36.0ms	(/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

455.0ms	(/ 1 (/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a)))))
25.0ms	(+ (+ (* z b) y) (* z (- y)))
40.0ms	(+ (* x y) (* z (- t a)))
92.0ms	(/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a))))

simplify635.0ms

Counts

159 → 159

Iterations

Useful iterations: done (630.0ms)

Iter	Nodes	Cost
0	223	4778
1	556	4332
2	1607	3985
done	5000	3624

prune394.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(+ (* z (- b y)) y)
1.3b	(+ (* x y) (* z (- t a)))
25.9b	(/ (+ (* x y) (* z (- t a))) (+ (* z (- b y)) y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `distribute-rgt-in` `sub-neg` `distribute-lft-in`
5×	`associate-r`
4×	`associate-+l+` `associate-+r+` `flip3-+` `flip-+`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`+-commutative` `associate-*r/` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

9.0ms	(* z (- b y))
5.0ms	(+ (* z (- b y)) y)
3.0ms	(+ (* x y) (* z (- t a)))
16.0ms	(/ (+ (* x y) (* z (- t a))) (+ (* z (- b y)) y))

series424.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* z (- b y))
30.0ms	(+ (* z (- b y)) y)
40.0ms	(+ (* x y) (* z (- t a)))
320.0ms	(/ (+ (* x y) (* z (- t a))) (+ (* z (- b y)) y))

simplify1.5s

Counts

99 → 99

Iterations

Useful iterations: 3 (468.0ms)

Iter	Nodes	Cost
0	146	1501
1	353	1455
2	1051	1331
3	4215	1327
done	5000	1327

prune264.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.5b

regimes541.0ms

Accuracy

24.6% (9.5b remaining)

Error of 20.4b against oracle of 10.9b and baseline of 23.5b

bsearch99.0ms

Steps

Iters	Range		Point
9	1.5247250177203267e+35	7.86294764107312e+43	7.736950116967238e+43
8	-1.4335373150418553e+75	-4.5705223523792306e+70	-7.710255796225628e+72

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	41
1	36	33
done	36	33

end0.0ms

sample838.0ms

Algorithm

intervals

Results

559.0ms

8392×

body

valid