Details

sample58.0ms

Algorithm

intervals

Results

25.0ms	241×	body	80	valid
3.0ms	12×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	5×	body	1280	valid
1.0ms	8×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (49.0ms)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.2b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite41.0ms

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:

37.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series405.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ (- t z) (- a t))
324.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.6s

Counts

70 → 70

Iterations

Useful iterations: 3 (833.0ms)

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

prune298.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
4.2b	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

rewrite133.0ms

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))
97.0ms	(* (- t z) (/ 1 (- a t)))
1.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

series437.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ 1 (- a t))
67.0ms	(* (- t z) (/ 1 (- a t)))
325.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

simplify5.8s

Counts

114 → 114

Iterations

Useful iterations: done (5.8s)

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

prune428.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
7.6b	(fma (* (* (- t z) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) y (+ x y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 106

Calls

4 calls:

14.0ms	(cbrt (/ 1 (- a t)))
7.0ms	(cbrt (/ 1 (- a t)))
7.0ms	(cbrt (/ 1 (- a t)))
0.0ms	(fma (* (* (- t z) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) y (+ x y))

series933.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt (/ 1 (- a t)))
223.0ms	(cbrt (/ 1 (- a t)))
244.0ms	(cbrt (/ 1 (- a t)))
262.0ms	(fma (* (* (- t z) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) y (+ x y))

simplify1.3s

Counts

118 → 118

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	141	1825
1	253	1639
2	607	1413
3	2181	1351
done	5000	1311

prune491.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.2b

localize30.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (* (* (cbrt (/ (- t z) (- a t))) (cbrt (/ (- t z) (- a t)))) (cbrt (/ (- t z) (- a t)))) y (+ x y))
3.6b	(cbrt (/ (- t z) (- a t)))
3.6b	(cbrt (/ (- t z) (- a t)))
3.6b	(cbrt (/ (- t z) (- a t)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 136

Calls

4 calls:

0.0ms	(fma (* (* (cbrt (/ (- t z) (- a t))) (cbrt (/ (- t z) (- a t)))) (cbrt (/ (- t z) (- a t)))) y (+ x y))
12.0ms	(cbrt (/ (- t z) (- a t)))
10.0ms	(cbrt (/ (- t z) (- a t)))
14.0ms	(cbrt (/ (- t z) (- a t)))

series1.4s

Counts

4 → 12

Calls

4 calls:

292.0ms	(fma (* (* (cbrt (/ (- t z) (- a t))) (cbrt (/ (- t z) (- a t)))) (cbrt (/ (- t z) (- a t)))) y (+ x y))
362.0ms	(cbrt (/ (- t z) (- a t)))
356.0ms	(cbrt (/ (- t z) (- a t)))
369.0ms	(cbrt (/ (- t z) (- a t)))

simplify965.0ms

Counts

148 → 148

Iterations

Useful iterations: done (956.0ms)

Iter	Nodes	Cost
0	140	2613
1	249	2523
2	454	2237
3	1190	2190
done	5000	2178

prune767.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.2b

regimes469.0ms

Accuracy

45.1% (4.7b remaining)

Error of 8.2b against oracle of 3.6b and baseline of 12.0b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	87
1	32	87
done	32	87

end0.0ms

sample1.9s

Algorithm

intervals

Results

614.0ms	7263×	body	80	valid
507.0ms	421×	body	320	valid
100.0ms	470×	body	640	valid
73.0ms	272×	body	1280	valid
32.0ms	272×	body	160	valid
5.0ms	16×	body	2560	valid