Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	265×	body	80	valid
2.0ms	14×	body	640	valid
2.0ms	12×	body	1280	valid
1.0ms	12×	body	320	valid
0.0ms	1×	body	2560	valid
0.0ms	3×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	45	12
3	122	12
4	303	12
5	741	12
6	1650	12
7	3370	12
done	5000	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.0b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.4b	(* (- y z) (/ (- t x) (- a z)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`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/`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
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 → 128

Calls

3 calls:

12.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
34.0ms	(* (- y z) (/ (- t x) (- a z)))

series335.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- t x) (- a z))
153.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
130.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify667.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	189	1881
1	491	1769
2	1932	1659
done	5000	1659

prune355.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.8b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
28×	`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`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 145

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
79.0ms	(* (/ (- 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)))))

series754.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (- a z))
151.0ms	(cbrt (- a z))
297.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
156.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.1s

Counts

157 → 157

Iterations

Useful iterations: 2 (245.0ms)

Iter	Nodes	Cost
0	261	3480
1	758	3305
2	3234	2736
done	5000	2736

prune525.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.4b

localize22.0ms

Local error

Found 4 expressions with local error:

3.5b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
3.5b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
3.5b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
8.0b	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`cbrt-div`
24×	`associate-/r/`
18×	`flip3--` `flip--`
17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`frac-times`
11×	`add-cube-cbrt`
6×	`associate-r/` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `pow1/3` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 100

Calls

4 calls:

10.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
10.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
11.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

372.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
368.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
363.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
160.0ms	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

simplify1.5s

Counts

112 → 112

Iterations

Useful iterations: 3 (400.0ms)

Iter	Nodes	Cost
0	172	3419
1	387	3300
2	1039	2614
3	4134	2495
done	5000	2495

prune511.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
10.1b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
33×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`associate-l`
14×	`cbrt-div` `distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 131

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(cbrt x)
79.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series824.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt x)
177.0ms	(cbrt x)
304.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
163.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify904.0ms

Counts

143 → 143

Iterations

Useful iterations: done (900.0ms)

Iter	Nodes	Cost
0	232	3101
1	653	2999
2	2822	2400
done	5000	2392

prune489.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.0b

regimes338.0ms

Accuracy

18.9% (8.1b remaining)

Error of 11.5b against oracle of 3.4b and baseline of 13.4b

bsearch87.0ms

Steps

Iters	Range		Point
5	4.4364499888015587e-184	1.690105319616841e-183	1.2686345652321895e-183
8	-1.3832302968011816e-77	-7.46084427730258e-82	-2.564733602818418e-81

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	115
1	44	115
done	44	115

end0.0ms

sample707.0ms

Algorithm

intervals

Results

255.0ms	7765×	body	80	valid
61.0ms	468×	body	640	valid
42.0ms	287×	body	1280	valid
40.0ms	451×	body	320	valid
16.0ms	265×	body	160	valid
5.0ms	30×	body	2560	valid