Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

268×

body

valid

simplify744.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	17
1	23	17
2	35	17
3	60	17
4	101	17
5	190	17
6	406	17
7	937	17
8	2703	17
done	5000	17

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 8.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* t z) x)
0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
0.2b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
10.7b	(/ (- (* y z) x) (- (* t z) x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
25×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`distribute-lft-out`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-/r` `associate-/l`
4×	`pow1` `div-sub` `associate-/r/` `associate-/l/`
3×	`flip3--` `flip3-+` `flip--` `flip-+`
2×	`cbrt-undiv` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log`

Counts

4 → 98

Calls

4 calls:

4.0ms	(- (* t z) x)
12.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
17.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
17.0ms	(/ (- (* y z) x) (- (* t z) x))

series95.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* t z) x)
28.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
42.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
20.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify854.0ms

Counts

110 → 110

Iterations

Useful iterations: done (851.0ms)

Iter	Nodes	Cost
0	157	2130
1	398	2046
2	1178	1920
3	3580	1916
done	5000	1913

prune395.0ms

Filtered

81 candidates to 110 candidates (-35.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 1.0b

Counts

111 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
0.2b	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
0.7b	(/ 1 (- (* t z) x))
10.1b	(* (- (* y z) x) (/ 1 (- (* t z) x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
29×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`associate-r`
13×	`add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`flip3--` `prod-exp` `flip--` `distribute-lft-out`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 121

Calls

4 calls:

3.0ms	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
8.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
9.0ms	(/ 1 (- (* t z) x))
14.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
38.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
7.0ms	(/ 1 (- (* t z) x))
19.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

simplify487.0ms

Counts

133 → 133

Iterations

Useful iterations: done (484.0ms)

Iter	Nodes	Cost
0	188	2549
1	475	2219
2	1668	2009
done	5002	2007

prune157.0ms

Filtered

86 candidates to 133 candidates (-54.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 1.0b

Counts

143 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (- (* y z) x))
8.8b	(cbrt (- (* t z) x))
8.8b	(cbrt (- (* t z) x))
8.8b	(cbrt (- (* t z) x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (- (* y z) x))
4.0ms	(cbrt (- (* t z) x))
4.0ms	(cbrt (- (* t z) x))
5.0ms	(cbrt (- (* t z) x))

series146.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt (- (* y z) x))
36.0ms	(cbrt (- (* t z) x))
38.0ms	(cbrt (- (* t z) x))
37.0ms	(cbrt (- (* t z) x))

simplify997.0ms

Counts

64 → 64

Iterations

Useful iterations: 4 (476.0ms)

Iter	Nodes	Cost
0	110	860
1	247	828
2	634	768
3	1625	724
4	3952	680
done	5001	680

prune110.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Merged error: 1.0b

Counts

73 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
10.7b	(/ (- (* y z) x) (- (* t z) x))
10.7b	(/ (- (* y z) x) (- (* t z) x))
10.7b	(/ (- (* y z) x) (- (* t z) x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
43×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`cbrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
8×	`associate-/r/` `distribute-lft-out`
6×	`flip3--` `flip--` `associate-/l/`
4×	`pow1` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num`
1×	`cbrt-div` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 127

Calls

4 calls:

15.0ms	(cbrt (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
10.0ms	(/ (- (* y z) x) (- (* t z) x))
11.0ms	(/ (- (* y z) x) (- (* t z) x))
11.0ms	(/ (- (* y z) x) (- (* t z) x))

series141.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
22.0ms	(/ (- (* y z) x) (- (* t z) x))
19.0ms	(/ (- (* y z) x) (- (* t z) x))
19.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify680.0ms

Counts

139 → 139

Iterations

Useful iterations: done (668.0ms)

Iter	Nodes	Cost
0	162	2830
1	346	2770
2	937	2592
3	2677	2570
done	5000	2564

prune260.0ms

Filtered

110 candidates to 139 candidates (-26.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	139	9	148

Merged error: 1.0b

Counts

148 → 9

regimes480.0ms

Accuracy

56.8% (2.9b remaining)

Error of 4.0b against oracle of 1.1b and baseline of 7.8b

bsearch49.0ms

Steps

Iters	Range		Point
9	9624807603436.258	2.1235669748025403e+20	2.0884824622682512e+20
9	-3.817206138481307e+76	-1.5116149063123207e+67	-7.058580885156793e+74

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	45
1	35	37
done	35	37

end0.0ms

sample862.0ms

Algorithm

intervals

Results

435.0ms

8332×

body

valid

Details

sample31.0ms

simplify744.0ms

prune4.0ms

localize12.0ms

rewrite53.0ms

series95.0ms

simplify854.0ms

prune395.0ms

localize13.0ms

rewrite38.0ms

series94.0ms

simplify487.0ms

prune157.0ms

localize20.0ms

rewrite19.0ms

series146.0ms

simplify997.0ms

prune110.0ms

localize19.0ms

rewrite51.0ms

series141.0ms

simplify680.0ms

prune260.0ms

regimes480.0ms

bsearch49.0ms

simplify3.0ms

end0.0ms

sample862.0ms

Profiling