Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	244×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify7.8s

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: 16.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.7b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite51.0ms

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))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
30.0ms	(* (- y z) (/ (- t x) (- a z)))

series328.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (- t x) (- a z))
151.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
128.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify909.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	183	1813
1	474	1704
2	1687	1606
done	5001	1606

prune319.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
5.2b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
5.7b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite70.0ms

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:

7.0ms	(/ 1 (- a z))
22.0ms	(* (- t x) (/ 1 (- a z)))
3.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
31.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1 (- a z))
52.0ms	(* (- t x) (/ 1 (- a z)))
151.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
129.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify883.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (217.0ms)

Iter	Nodes	Cost
0	221	2286
1	586	1896
2	2094	1716
done	5000	1716

prune353.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.7b	(+ x (* (- y z) (pow (/ (- t x) (- a z)) 1)))
5.7b	(* (- y z) (pow (/ (- t x) (- a z)) 1))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
35×	`associate-r`
33×	`unpow-prod-down`
28×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
13×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
4×	`pow1` `flip3--` `prod-exp` `associate-/r/` `flip--` `unswap-sqr`
2×	`div-exp` `associate-*l/` `pow-exp` `div-inv` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

3 → 123

Calls

3 calls:

10.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (pow (/ (- t x) (- a z)) 1)))
59.0ms	(* (- y z) (pow (/ (- t x) (- a z)) 1))

series334.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- t x) (- a z))
154.0ms	(+ x (* (- y z) (pow (/ (- t x) (- a z)) 1)))
128.0ms	(* (- y z) (pow (/ (- t x) (- a z)) 1))

simplify791.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (313.0ms)

Iter	Nodes	Cost
0	216	2028
1	521	1741
2	1873	1662
done	5001	1662

prune347.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
5.7b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x)))))
10.8b	(+ x (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x))))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac`
69×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
51×	`associate-r`
36×	`cbrt-prod`
27×	`add-cube-cbrt`
22×	`add-exp-log`
16×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
7×	`prod-exp` `cbrt-unprod`
6×	`pow1` `cbrt-undiv` `cbrt-div` `div-exp` `add-log-exp`
5×	`flip3--` `associate-l` `flip--`
4×	`unswap-sqr`
3×	`associate-/r/`
2×	`frac-times` `pow1/3` `associate-*l/` `div-inv`
1×	`+-commutative` `flip3-+` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip-+`

Counts

4 → 125

Calls

4 calls:

2.0ms	(cbrt (- t x))
2.0ms	(cbrt (- t x))
64.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x)))))
3.0ms	(+ x (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x))))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (- t x))
145.0ms	(cbrt (- t x))
132.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x)))))
154.0ms	(+ x (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x))))))

simplify1.0s

Counts

137 → 137

Iterations

Useful iterations: 2 (424.0ms)

Iter	Nodes	Cost
0	289	2899
1	727	2726
2	2805	2172
done	5001	2172

prune379.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.8b

regimes308.0ms

Accuracy

18.6% (6.3b remaining)

Error of 10.5b against oracle of 4.3b and baseline of 12.0b

bsearch117.0ms

Steps

Iters	Range		Point
9	6.606479948802491e-148	7.906484867512465e-140	2.554699244011774e-147
8	-1.1766157657047581e-163	-1.090162501590038e-166	-3.6771152743398664e-164

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	32	117
1	41	70
done	41	70

end0.0ms

sample706.0ms

Algorithm

intervals

Results

263.0ms	7829×	body	80	valid
58.0ms	490×	body	640	valid
45.0ms	283×	body	1280	valid
36.0ms	401×	body	320	valid
15.0ms	240×	body	160	valid
3.0ms	18×	body	2560	valid