Details

sample63.0ms

Algorithm

intervals

Results

18.0ms	243×	body	80	valid
5.0ms	19×	body	640	valid
3.0ms	13×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	7×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
14.6b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite21.0ms

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:

19.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series220.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(/ (- t x) (- a z))
132.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.0s

Counts

70 → 70

Iterations

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

prune500.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.6b	(* (- y z) (/ (- t x) (- a z)))

rewrite115.0ms

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:

36.0ms	(/ (- t x) (- a z))
13.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
58.0ms	(* (- y z) (/ (- t x) (- a z)))

series531.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (- t x) (- a z))
257.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
200.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.8s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	2719
1	515
0	189

prune886.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.0b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite224.0ms

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:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
193.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
18.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

240.0ms	(cbrt (- a z))
223.0ms	(cbrt (- a z))
469.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
235.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.5s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	3757
1	771
0	261

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.0b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
8.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

124×	`cbrt-div`
58×	`add-exp-log`
38×	`add-cbrt-cube`
35×	`flip3--` `associate-r` `flip--`
34×	`associate-/r/`
33×	`frac-times`
25×	`prod-exp` `cbrt-unprod`
23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp` `associate-l` `associate-*l/`
11×	`times-frac` `associate-*r/` `add-cube-cbrt`
10×	`cbrt-prod`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-def`
2×	`pow1/3` `div-inv` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 142

Calls

4 calls:

7.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
350.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
12.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt (- a z))
235.0ms	(cbrt (- a z))
488.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
237.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

simplify1.7s

Counts

154 → 154

Iterations

Iter	Nodes
done	5000
2	4182
1	1021
0	322

prune1.1s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.1b

regimes782.0ms

Accuracy

28% (6.4b remaining)

Error of 10.1b against oracle of 3.7b and baseline of 12.6b

bsearch189.0ms

Steps

Iters	Range		Point
9	1.528893720358808e-127	9.112270346435697e-122	1.3787287431407374e-126
8	-8.778032766378265e-192	-1.9835161528811826e-194	-4.016598119805832e-193

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	7819×	body	80	valid
100.0ms	479×	body	640	valid
71.0ms	272×	body	1280	valid
63.0ms	402×	body	320	valid
41.0ms	16×	body	2560	valid
27.0ms	258×	body	160	valid