Details

sample77.0ms

Algorithm

intervals

Results

19.0ms	250×	body	80	valid
3.0ms	15×	body	320	valid
3.0ms	10×	body	640	valid
1.0ms	4×	body	1280	valid
1.0ms	6×	body	160	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2162
5	786
4	312
3	120
2	44
1	23
0	11

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize49.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.5b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.5b	(* (- y z) (/ (- t x) (- a z)))

rewrite233.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-l` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`insert-posit16`
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 → 122

Calls

3 calls:

57.0ms	(/ (- t x) (- a z))
22.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
133.0ms	(* (- y z) (/ (- t x) (- a z)))

series853.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (- t x) (- a z))
463.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
297.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify3.1s

Counts

131 → 131

Iterations

Iter	Nodes
done	5005
2	1774
1	503
0	186

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.0b

localize124.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.2b	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
6.4b	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cbrt-cube`
10×	`cbrt-prod`
9×	`cbrt-undiv` `div-exp`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`pow1` `cbrt-div` `prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `associate-/r/` `flip--`
2×	`pow1/3` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `flip3-+` `div-sub` `associate-l/` `associate-*r/` `flip-+` `div-inv`

Counts

4 → 82

Calls

4 calls:

6.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
73.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
18.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

279.0ms	(cbrt (- a z))
326.0ms	(cbrt (- a z))
1.5s	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
305.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify3.5s

Counts

94 → 94

Iterations

Iter	Nodes
done	5003
2	1626
1	555
0	215

prune1.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.3b

localize256.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.2b	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x)))))
6.7b	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
19×	`add-cbrt-cube`
16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`cbrt-undiv` `div-exp`
10×	`cbrt-prod`
8×	`prod-exp` `add-cube-cbrt` `cbrt-unprod`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`pow1` `cbrt-div` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `associate-/r/` `flip--`
2×	`pow1/3` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `flip3-+` `div-sub` `associate-l/` `associate-*r/` `flip-+` `div-inv`

Counts

4 → 86

Calls

4 calls:

12.0ms	(cbrt (- a z))
12.0ms	(cbrt (- a z))
127.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x)))))
10.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt (- a z))
309.0ms	(cbrt (- a z))
1.5s	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x)))))
369.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify5.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	2240
1	661
0	242

prune2.0s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 2.3b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
5.7b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite346.0ms

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`
4×	`insert-posit16`
3×	`associate-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 138

Calls

4 calls:

12.0ms	(cbrt (- a z))
12.0ms	(cbrt (- a z))
280.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
13.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt (- a z))
300.0ms	(cbrt (- a z))
638.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
368.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify6.0s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2909
1	750
0	258

prune2.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.3b

regimes2.3s

Accuracy

21.4% (6.8b remaining)

Error of 10.2b against oracle of 3.4b and baseline of 12.1b

bsearch213.0ms

Steps

Iters	Range		Point
8	5.108312120969135e-178	5.5104307175624145e-174	1.082916304047229e-175
8	-4.535093393717798e-77	-8.512415071153562e-82	-2.0167221434791827e-79

simplify29.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample1.6s

Algorithm

intervals

Results

546.0ms	7809×	body	80	valid
170.0ms	463×	body	640	valid
126.0ms	411×	body	320	valid
102.0ms	284×	body	1280	valid
33.0ms	11×	body	2560	valid
27.0ms	252×	body	160	valid