Details

sample40.0ms

Algorithm

intervals

Results

10.0ms	250×	body	80	valid
3.0ms	16×	body	1280	valid
2.0ms	15×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.9b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.0b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite49.0ms

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:

44.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series232.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- t x) (- a z))
165.0ms	(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

prune520.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
3.8b	(* (- y z) (/ (- t x) (- a z)))

rewrite114.0ms

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:

31.0ms	(/ (- t x) (- a z))
9.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
66.0ms	(* (- y z) (/ (- t x) (- a z)))

series435.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (- t x) (- a z))
182.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
194.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify2.1s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	2719
1	515
0	189

prune910.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

localize96.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
10.9b	(+ x (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`fma-def` `flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 67

Calls

4 calls:

7.0ms	(cbrt (- a z))
7.0ms	(cbrt (- a z))
7.0ms	(cbrt (- a z))
14.0ms	(+ x (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series905.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(cbrt (- a z))
210.0ms	(cbrt (- a z))
227.0ms	(cbrt (- a z))
254.0ms	(+ x (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify2.9s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4550
2	860
1	268
0	111

prune801.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

localize89.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
12.0b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series863.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(cbrt (- a z))
182.0ms	(cbrt (- a z))
176.0ms	(cbrt (- a z))
288.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify1.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1886
2	531
1	208
0	101

prune645.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.6b

regimes1.1s

Accuracy

55% (3.8b remaining)

Error of 7.2b against oracle of 3.4b and baseline of 11.9b

bsearch5.0ms

simplify19.0ms

Iterations

Iter	Nodes
done	40
1	40
0	31

end0.0ms

sample1.9s

Algorithm

intervals

Results

532.0ms	7893×	body	80	valid
483.0ms	375×	body	320	valid
134.0ms	322×	body	1280	valid
78.0ms	429×	body	640	valid
49.0ms	260×	body	160	valid
5.0ms	19×	body	2560	valid