Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	242×	body	80	valid
5.0ms	16×	body	640	valid
4.0ms	15×	body	320	valid
3.0ms	8×	body	1280	valid
1.0ms	9×	body	160	valid

simplify16.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	44	13
3	122	13
4	327	13
5	732	13
6	1485	13
7	2361	13
8	3197	13
9	3665	13
10	3837	13
11	4148	13
12	4410	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.9b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.0b	(* (- y z) (/ (- t x) (- a z)))

rewrite101.0ms

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:

23.0ms	(/ (- t x) (- a z))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
66.0ms	(* (- y z) (/ (- t x) (- a z)))

series448.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- t x) (- a z))
213.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
156.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify911.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (307.0ms)

Iter	Nodes	Cost
0	183	1813
1	469	1704
2	1736	1606
done	5000	1606

prune376.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.6b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.3b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite247.0ms

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:

5.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
210.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
20.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt (- a z))
166.0ms	(cbrt (- a z))
423.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
236.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.7s

Counts

146 → 146

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	255	3364
1	722	3180
2	2785	2663
done	5000	2496

prune574.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.3b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.1b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
166×	`add-sqr-sqrt`
115×	`cbrt-prod`
103×	`*-un-lft-identity`
80×	`associate-l`
76×	`cbrt-div`
61×	`associate-r`
59×	`add-cube-cbrt`
42×	`associate-/r/`
36×	`add-exp-log`
33×	`flip3--` `flip--`
22×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
21×	`frac-times`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
11×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
6×	`pow1` `div-inv` `add-log-exp`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 230

Calls

4 calls:

5.0ms	(cbrt (- a z))
7.0ms	(cbrt (- a z))
367.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
12.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series985.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (- a z))
197.0ms	(cbrt (- a z))
381.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
210.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify2.2s

Counts

242 → 242

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	437	8451
1	1311	8144
2	4714	7728
done	5000	7622

prune1.3s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
4.0b	(* (- y z) (* (- t x) (/ 1 (- a z))))
5.2b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

rewrite182.0ms

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:

17.0ms	(/ 1 (- a z))
71.0ms	(* (- t x) (/ 1 (- a z)))
78.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
10.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1 (- a z))
58.0ms	(* (- t x) (/ 1 (- a z)))
185.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
188.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

simplify1.2s

Counts

158 → 158

Iterations

Useful iterations: 2 (372.0ms)

Iter	Nodes	Cost
0	221	2286
1	563	1896
2	2122	1716
done	5000	1716

prune413.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 4.7b

regimes412.0ms

Accuracy

18.8% (6.7b remaining)

Error of 11.1b against oracle of 4.3b and baseline of 12.6b

bsearch172.0ms

Steps

Iters	Range		Point
11	3.7544747272031375e-180	4.954485790139649e-158	1.5108530635732106e-160
9	-4.494716191071896e-101	-1.1624215725433809e-108	-1.3179146429479965e-107

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	81
1	39	81
done	39	81

end0.0ms

sample1.5s

Algorithm

intervals

Results

693.0ms	7745×	body	80	valid
149.0ms	482×	body	640	valid
105.0ms	441×	body	320	valid
74.0ms	261×	body	1280	valid
33.0ms	278×	body	160	valid
4.0ms	12×	body	2560	valid