Details

sample63.0ms

Algorithm

intervals

Results

20.0ms	130×	body	80	valid
13.0ms	46×	body	1280	valid
10.0ms	44×	body	640	valid
4.0ms	21×	body	320	valid
2.0ms	15×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	79	13
9	183	13
10	535	13
11	1706	13
12	3584	13
done	5000	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ 1.0 x) (- x 1.0))
3.8b	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

24.0ms	(/ x (+ x 1.0))
59.0ms	(/ (+ 1.0 x) (- x 1.0))
187.0ms	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

series309.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ x (+ x 1.0))
75.0ms	(/ (+ 1.0 x) (- x 1.0))
171.0ms	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

simplify3.0s

Counts

605 → 605

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	536	34216
1	1303	30941
2	4755	23491
done	5000	23490

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 1.0 x) (- x 1.0))
0.0b	(pow (/ x (+ x 1.0)) 3)
3.8b	(- (cbrt (pow (/ x (+ x 1.0)) 3)) (/ (+ 1.0 x) (- x 1.0)))
19.2b	(cbrt (pow (/ x (+ x 1.0)) 3))

rewrite740.0ms

Algorithm

rewrite-expression-head

Rules

2167×	`*-un-lft-identity`
1627×	`times-frac`
1392×	`add-sqr-sqrt`
1188×	`cbrt-prod`
1170×	`prod-diff`
985×	`add-cube-cbrt`
526×	`unpow-prod-down` `cube-prod`
405×	`distribute-lft-out`
208×	`associate-/r/`
199×	`difference-of-squares`
186×	`distribute-lft-out--`
104×	`div-inv`
59×	`flip3-+` `flip-+`
47×	`flip3--` `flip--`
45×	`fma-neg`
31×	`sqr-pow`
29×	`cube-mult` `unpow3`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cube-div` `pow-unpow`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `frac-sub` `rem-cbrt-cube`

Counts

4 → 1404

Calls

4 calls:

35.0ms	(/ (+ 1.0 x) (- x 1.0))
27.0ms	(pow (/ x (+ x 1.0)) 3)
432.0ms	(- (cbrt (pow (/ x (+ x 1.0)) 3)) (/ (+ 1.0 x) (- x 1.0)))
15.0ms	(cbrt (pow (/ x (+ x 1.0)) 3))

series418.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (+ 1.0 x) (- x 1.0))
83.0ms	(pow (/ x (+ x 1.0)) 3)
190.0ms	(- (cbrt (pow (/ x (+ x 1.0)) 3)) (/ (+ 1.0 x) (- x 1.0)))
93.0ms	(cbrt (pow (/ x (+ x 1.0)) 3))

simplify1.5s

Counts

1416 → 1416

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	806	91756
1	2079	74754
done	5002	65048

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- x 1.0))
0.6b	(/ 1 (* (+ x 1.0) (+ x 1.0)))
13.3b	(cbrt (/ 1 (* (+ x 1.0) (+ x 1.0))))
29.8b	(fma (cbrt (/ 1 (* (+ x 1.0) (+ x 1.0)))) (/ x (cbrt (+ x 1.0))) (- (pow (/ (cbrt (+ 1.0 x)) (cbrt (- x 1.0))) 3)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
16×	`associate-/r/`
15×	`add-exp-log`
12×	`pow1` `flip3-+` `flip-+`
11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `add-cbrt-cube`
8×	`frac-times`
6×	`pow-flip` `times-frac`
4×	`expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `prod-exp` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `pow1/3` `1-exp` `div-inv`
1×	`pow2` `flip3--` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

8.0ms	(cbrt (- x 1.0))
37.0ms	(/ 1 (* (+ x 1.0) (+ x 1.0)))
34.0ms	(cbrt (/ 1 (* (+ x 1.0) (+ x 1.0))))
0.0ms	(fma (cbrt (/ 1 (* (+ x 1.0) (+ x 1.0)))) (/ x (cbrt (+ x 1.0))) (- (pow (/ (cbrt (+ 1.0 x)) (cbrt (- x 1.0))) 3)))

series781.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (- x 1.0))
39.0ms	(/ 1 (* (+ x 1.0) (+ x 1.0)))
184.0ms	(cbrt (/ 1 (* (+ x 1.0) (+ x 1.0))))
403.0ms	(fma (cbrt (/ 1 (* (+ x 1.0) (+ x 1.0)))) (/ x (cbrt (+ x 1.0))) (- (pow (/ (cbrt (+ 1.0 x)) (cbrt (- x 1.0))) 3)))

simplify1.8s

Counts

107 → 107

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	277	1825
1	703	1695
2	3124	1483
done	5001	1470

prune591.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
0.0b	(/ (+ 1.0 x) (- x 1.0))
5.4b	(/ x (+ (pow x 3) (pow 1.0 3)))
30.3b	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ (+ 1.0 x) (- x 1.0))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
47×	`times-frac`
39×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
26×	`distribute-lft-out`
16×	`unpow-prod-down` `cube-prod`
14×	`associate-/r*`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `sum-cubes` `log1p-expm1-u`
3×	`associate-+r+` `flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3--` `fma-def` `diff-log` `prod-diff` `flip--` `fma-udef`

Counts

4 → 131

Calls

4 calls:

25.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
60.0ms	(/ (+ 1.0 x) (- x 1.0))
59.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
0.0ms	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ (+ 1.0 x) (- x 1.0))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
43.0ms	(/ (+ 1.0 x) (- x 1.0))
127.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
242.0ms	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ (+ 1.0 x) (- x 1.0))))

simplify3.4s

Counts

143 → 143

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	237	2271
1	621	2019
2	3086	1858
done	5000	1848

prune609.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes53.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch125.0ms

Steps

Iters	Range		Point
8	1575.9184687212278	8587103.50349991	12201.687510237365
10	-1.3980170606481126e+18	-1333.496421940221	-20084.465704431863

simplify17.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	110
1	48	95
2	58	95
3	63	95
4	66	95
done	66	95

end0.0ms

sample1.3s

Algorithm

intervals

Results

365.0ms	1699×	body	1280	valid
350.0ms	4137×	body	80	valid
272.0ms	1218×	body	640	valid
70.0ms	602×	body	320	valid
27.0ms	344×	body	160	valid