Details

sample59.0ms

Algorithm

intervals

Results

17.0ms	232×	body	80	valid
5.0ms	18×	body	640	valid
3.0ms	16×	body	320	valid
2.0ms	7×	body	1280	valid
0.0ms	3×	body	160	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (77.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	110	13
4	239	12
5	729	12
6	3426	12
done	5000	12

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.3b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.7b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite58.0ms

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-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

53.0ms	(/ (- t z) (- a t))
1.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series377.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- t z) (- a t))
304.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify3.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	113	906
1	263	878
2	819	828
3	4388	824
done	5000	824

prune624.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
2.9b	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 105

Calls

3 calls:

27.0ms	(/ 1 (- a t))
100.0ms	(* (- t z) (/ 1 (- a t)))
1.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

series500.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ 1 (- a t))
77.0ms	(* (- t z) (/ 1 (- a t)))
354.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

simplify8.9s

Counts

114 → 114

Iterations

Useful iterations: done (8.9s)

Iter	Nodes	Cost
0	149	1273
1	357	1117
2	2932	942
done	5001	936

prune753.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.1b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- t z))
0.3b	(/ 1 (/ (- a t) (- t z)))
1.7b	(fma (/ 1 (/ (- a t) (- t z))) y (+ x y))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

49.0ms	(/ (- a t) (- t z))
45.0ms	(/ 1 (/ (- a t) (- t z)))
1.0ms	(fma (/ 1 (/ (- a t) (- t z))) y (+ x y))

series461.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (- a t) (- t z))
218.0ms	(/ 1 (/ (- a t) (- t z)))
153.0ms	(fma (/ 1 (/ (- a t) (- t z))) y (+ x y))

simplify2.6s

Counts

223 → 223

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	272	3776
1	713	3262
2	3985	3055
done	5000	3051

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- t z))
0.2b	(* (- a t) (/ 1 (- t z)))
0.3b	(/ 1 (* (- a t) (/ 1 (- t z))))
2.9b	(fma (/ 1 (* (- a t) (/ 1 (- t z)))) y (+ x y))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`div-exp` `add-cbrt-cube`
16×	`prod-exp`
10×	`pow1` `rec-exp` `1-exp` `associate-/r/`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `flip3--` `associate-/r` `flip--` `associate-/l`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `un-div-inv` `inv-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 151

Calls

4 calls:

20.0ms	(/ 1 (- t z))
73.0ms	(* (- a t) (/ 1 (- t z)))
72.0ms	(/ 1 (* (- a t) (/ 1 (- t z))))
1.0ms	(fma (/ 1 (* (- a t) (/ 1 (- t z)))) y (+ x y))

series573.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1 (- t z))
106.0ms	(* (- a t) (/ 1 (- t z)))
251.0ms	(/ 1 (* (- a t) (/ 1 (- t z))))
149.0ms	(fma (/ 1 (* (- a t) (/ 1 (- t z)))) y (+ x y))

simplify5.9s

Counts

163 → 163

Iterations

Useful iterations: done (5.9s)

Iter	Nodes	Cost
0	195	1938
1	499	1565
2	3780	1313
done	5001	1301

prune866.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.1b

regimes780.0ms

Accuracy

33.7% (5.3b remaining)

Error of 8.6b against oracle of 3.2b and baseline of 11.3b

bsearch136.0ms

Steps

Iters	Range		Point
8	2.1459675436576726e+107	6.717228219612742e+109	1.0302980953989481e+108
7	-1.834776734297916e+156	-7.190704333723872e+154	-9.865242998422085e+154

simplify7.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	21	36
1	28	31
done	28	31

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	7401×	body	80	valid
158.0ms	396×	body	320	valid
150.0ms	436×	body	640	valid
92.0ms	251×	body	1280	valid
70.0ms	260×	body	160	valid
4.0ms	11×	body	2560	valid