Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	251×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4619
5	1129
4	367
3	128
2	46
1	23
0	11

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.0b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

46.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series216.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(/ (- t x) (- a z))
129.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.4s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4626
2	848
1	274
0	118

prune561.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.1b	(* (- y z) (/ (- t x) (- a z)))

rewrite119.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-l` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

30.0ms	(/ (- t x) (- a z))
6.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
73.0ms	(* (- y z) (/ (- t x) (- a z)))

series512.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ (- t x) (- a z))
247.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
195.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify2.2s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	2719
1	515
0	189

prune845.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 3.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite159.0ms

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-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 145

Calls

4 calls:

6.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
131.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series957.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt (- a z))
193.0ms	(cbrt (- a z))
337.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
229.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.7s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	3757
1	771
0	261

prune1.1s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.3b

localize104.0ms

Local error

Found 4 expressions with local error:

1.1b	(cbrt (/ (- t x) (cbrt (- a z))))
1.1b	(cbrt (/ (- t x) (cbrt (- a z))))
1.3b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z))))))
7.8b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

142×	`cbrt-prod`
101×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
86×	`times-frac`
45×	`add-cube-cbrt`
27×	`distribute-lft-out--` `difference-of-squares`
26×	`cbrt-div`
25×	`add-exp-log`
17×	`associate-l`
15×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`prod-exp` `cbrt-unprod`
9×	`frac-times` `pow1`
8×	`flip3--` `flip--`
7×	`associate-*r/`
6×	`add-log-exp`
5×	`associate-*l/`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down` `div-inv`
2×	`pow1/3` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `associate-r` `*-commutative` `flip-+`

Counts

4 → 181

Calls

4 calls:

9.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
10.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
190.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z))))))
11.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

318.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
337.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
433.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z))))))
212.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

simplify2.1s

Counts

193 → 193

Iterations

Iter	Nodes
done	5000
2	2985
1	853
0	351

prune1.4s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.3b

regimes1.2s

Accuracy

47.7% (5.0b remaining)

Error of 8.3b against oracle of 3.2b and baseline of 12.9b

bsearch4.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	33
1	33
0	30

end0.0ms

sample1.7s

Algorithm

intervals

Results

955.0ms	7814×	body	80	valid
99.0ms	484×	body	640	valid
92.0ms	414×	body	320	valid
66.0ms	252×	body	1280	valid
27.0ms	251×	body	160	valid
6.0ms	20×	body	2560	valid