Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	250×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	3×	body	1280	valid
0.0ms	1×	body	2560	valid

simplify8.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	43	13
3	115	13
4	263	13
5	568	13
6	1004	13
7	1712	13
8	3060	13
9	3795	13
10	3999	13
11	4453	13
done	5001	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.7b	(* (- y z) (/ (- t x) (- a z)))
4.3b	(+ x (* (- y z) (/ (- t x) (- a z))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

10.0ms	(/ (- t x) (- a z))
35.0ms	(* (- y z) (/ (- t x) (- a z)))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))

series336.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- t x) (- a z))
128.0ms	(* (- y z) (/ (- t x) (- a z)))
156.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))

simplify935.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (267.0ms)

Iter	Nodes	Cost
0	183	1813
1	474	1704
2	1686	1606
done	5000	1606

prune311.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
77.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series749.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
296.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
154.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify987.0ms

Counts

146 → 146

Iterations

Useful iterations: done (982.0ms)

Iter	Nodes	Cost
0	255	3364
1	743	3180
2	2872	2663
done	5001	2655

prune469.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
3.7b	(* (- y z) (* (- t x) (/ 1 (- a z))))
5.0b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 146

Calls

4 calls:

5.0ms	(/ 1 (- a z))
23.0ms	(* (- t x) (/ 1 (- a z)))
35.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
3.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
127.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
155.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

simplify833.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (220.0ms)

Iter	Nodes	Cost
0	221	2286
1	586	1896
2	2088	1716
done	5000	1716

prune326.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (/ (- t x) (- a z)))
5.7b	(cbrt (/ (- t x) (- a z)))
5.7b	(cbrt (/ (- t x) (- a z)))
8.4b	(+ x (* (- y z) (* (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z)))) (cbrt (/ (- t x) (- a z))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 131

Calls

4 calls:

5.0ms	(cbrt (/ (- t x) (- a z)))
5.0ms	(cbrt (/ (- t x) (- a z)))
5.0ms	(cbrt (/ (- t x) (- a z)))
3.0ms	(+ x (* (- y z) (* (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z)))) (cbrt (/ (- t x) (- a z))))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (/ (- t x) (- a z)))
150.0ms	(cbrt (/ (- t x) (- a z)))
149.0ms	(cbrt (/ (- t x) (- a z)))
153.0ms	(+ x (* (- y z) (* (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z)))) (cbrt (/ (- t x) (- a z))))))

simplify1.2s

Counts

143 → 143

Iterations

Useful iterations: 3 (384.0ms)

Iter	Nodes	Cost
0	183	2893
1	388	2774
2	883	2419
3	2775	2320
done	5001	2320

prune465.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.1b

regimes288.0ms

Accuracy

52.2% (4.4b remaining)

Error of 7.6b against oracle of 3.2b and baseline of 12.4b

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	80
1	34	80
done	34	80

end0.0ms

sample692.0ms

Algorithm

intervals

Results

269.0ms	7794×	body	80	valid
55.0ms	460×	body	640	valid
40.0ms	435×	body	320	valid
38.0ms	255×	body	1280	valid
17.0ms	280×	body	160	valid
3.0ms	14×	body	2560	valid