Details

sample39.0ms

Algorithm

intervals

Results

14.0ms	228×	body	80	valid
3.0ms	20×	body	320	valid
2.0ms	14×	body	640	valid
1.0ms	7×	body	1280	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	3757
7	2046
6	989
5	406
4	195
3	103
2	50
1	22
0	11

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
13.3b	(fma (- t z) (/ y (- a t)) (+ x y))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

9.0ms	(/ y (- a t))
0.0ms	(fma (- t z) (/ y (- a t)) (+ x y))

series222.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ y (- a t))
174.0ms	(fma (- t z) (/ y (- a t)) (+ x y))

simplify1.6s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	1426
2	444
1	174
0	92

prune426.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
4.0b	(+ (* (- t z) (/ y (- a t))) (+ x y))
8.7b	(* (- t z) (/ y (- a t)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-cbrt-cube` `frac-add` `add-exp-log`
8×	`flip3--` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
5×	`pow1` `associate-/r` `associate-l*`
4×	`associate-/r/`
3×	`expm1-log1p-u` `sum-log` `associate-r/` `log1p-expm1-u` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `clear-num` `fma-def` `frac-2neg` `pow-prod-down` `*-commutative`

Counts

3 → 113

Calls

3 calls:

10.0ms	(/ y (- a t))
25.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
54.0ms	(* (- t z) (/ y (- a t)))

series320.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ y (- a t))
187.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
97.0ms	(* (- t z) (/ y (- a t)))

simplify2.6s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	3029
1	672
0	214

prune957.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t z))
3.5b	(* (cbrt (- t z)) (/ y (- a t)))
5.3b	(* (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t))))
8.4b	(+ (* (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t)))) (+ x y))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

330×	`cbrt-div`
248×	`frac-times`
166×	`flip3--` `flip--`
116×	`associate-*l/`
106×	`frac-add`
79×	`associate-*r/`
54×	`flip3-+` `flip-+`
36×	`add-sqr-sqrt`
30×	`add-exp-log`
26×	`*-un-lft-identity`
22×	`associate-r`
18×	`pow1` `add-cbrt-cube`
17×	`times-frac`
16×	`add-cube-cbrt`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-prod`
9×	`associate-l` `pow-prod-down` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`cbrt-undiv` `sum-log` `div-exp`
2×	`associate-/r/` `*-commutative`
1×	`+-commutative` `associate-+r+` `fma-def` `pow1/3` `div-inv`

Counts

4 → 273

Calls

4 calls:

3.0ms	(cbrt (- t z))
46.0ms	(* (cbrt (- t z)) (/ y (- a t)))
146.0ms	(* (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t))))
140.0ms	(+ (* (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t)))) (+ x y))

series1.3s

Counts

4 → 12

Calls

4 calls:

261.0ms	(cbrt (- t z))
702.0ms	(* (cbrt (- t z)) (/ y (- a t)))
92.0ms	(* (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t))))
244.0ms	(+ (* (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t)))) (+ x y))

simplify3.0s

Counts

285 → 285

Iterations

Iter	Nodes
done	5003
1	2669
0	664

prune3.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t z))
0.6b	(cbrt (- t z))
3.5b	(* (cbrt (- t z)) (/ y (- a t)))
12.3b	(fma (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t))) (+ x y))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`associate-r`
17×	`cbrt-prod` `times-frac` `add-cube-cbrt`
9×	`add-exp-log`
8×	`cbrt-div` `associate-l`
7×	`add-cbrt-cube`
6×	`pow1` `distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`frac-times` `pow1/3` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 97

Calls

4 calls:

3.0ms	(cbrt (- t z))
3.0ms	(cbrt (- t z))
44.0ms	(* (cbrt (- t z)) (/ y (- a t)))
0.0ms	(fma (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t))) (+ x y))

series1.3s

Counts

4 → 12

Calls

4 calls:

212.0ms	(cbrt (- t z))
199.0ms	(cbrt (- t z))
566.0ms	(* (cbrt (- t z)) (/ y (- a t)))
283.0ms	(fma (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- t z)) (/ y (- a t))) (+ x y))

simplify2.2s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
3	3880
2	1152
1	429
0	180

prune741.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.5b

regimes813.0ms

Accuracy

33.4% (6.1b remaining)

Error of 9.1b against oracle of 3.0b and baseline of 12.2b

bsearch109.0ms

Steps

Iters	Range		Point
7	9.806112190462245e+179	1.1551355022400793e+182	9.944888148073561e+179
10	-9.698398649057306e+55	-1.4923929367486821e+46	-4.367546623917848e+55

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample1.3s

Algorithm

intervals

Results

536.0ms	7416×	body	80	valid
161.0ms	258×	body	1280	valid
121.0ms	430×	body	640	valid
58.0ms	402×	body	320	valid
31.0ms	255×	body	160	valid
5.0ms	16×	body	2560	valid