Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	233×	body	80	valid
5.0ms	15×	body	640	valid
3.0ms	7×	body	1280	valid
3.0ms	11×	body	320	valid
2.0ms	10×	body	160	valid

simplify13.2s

Counts

1 → 1

Iterations

Useful iterations: 4 (80.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	109	13
4	203	12
5	451	12
6	748	12
7	1078	12
8	1400	12
9	1655	12
10	2153	12
11	2683	12
12	3847	12
done	5001	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

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:

30.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series338.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- t z) (- a t))
282.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.3s

Counts

70 → 70

Iterations

Useful iterations: 3 (446.0ms)

Iter	Nodes	Cost
0	113	906
1	258	878
2	622	826
3	1643	824
done	5000	824

prune247.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.5b	(* (/ (- t z) (- a t)) y)
2.8b	(+ (* (/ (- t z) (- a t)) y) (+ x y))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 124

Calls

3 calls:

34.0ms	(/ (- t z) (- a t))
80.0ms	(* (/ (- t z) (- a t)) y)
50.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

series496.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (- t z) (- a t))
163.0ms	(* (/ (- t z) (- a t)) y)
275.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

simplify1.2s

Counts

133 → 133

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	195	1736
1	541	1646
2	1652	1560
done	5001	1549

prune514.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.1b	(+ (* (- t z) (/ y (- a t))) (+ x y))
12.4b	(* (- t z) (/ y (- a t)))

rewrite157.0ms

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

Counts

3 → 113

Calls

3 calls:

20.0ms	(/ y (- a t))
51.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
78.0ms	(* (- t z) (/ y (- a t)))

series379.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ y (- a t))
223.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
107.0ms	(* (- t z) (/ y (- a t)))

simplify1.9s

Counts

122 → 122

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	214	1838
1	635	1681
2	2750	1605
done	5000	1603

prune492.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(* (cbrt y) (cbrt y))
3.5b	(* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
8.9b	(+ (* (* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`add-exp-log` `frac-times`
22×	`associate-*l/` `frac-add`
19×	`cbrt-prod` `associate-r`
17×	`*-un-lft-identity`
16×	`flip3--` `flip--`
15×	`add-cube-cbrt`
14×	`add-cbrt-cube`
13×	`pow1`
12×	`cbrt-div` `flip3-+` `flip-+`
11×	`associate-l`
10×	`prod-exp` `cbrt-unprod`
9×	`associate-*r/` `add-log-exp`
8×	`associate-/r/`
7×	`pow1/3`
6×	`swap-sqr` `unswap-sqr`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`pow-prod-down` `sum-log`
2×	`times-frac` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `pow2` `associate-+r+` `fma-def` `pow-plus` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 139

Calls

4 calls:

2.0ms	(cbrt y)
19.0ms	(* (cbrt y) (cbrt y))
123.0ms	(* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
313.0ms	(+ (* (* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

series1.3s

Counts

4 → 12

Calls

4 calls:

296.0ms	(cbrt y)
323.0ms	(* (cbrt y) (cbrt y))
373.0ms	(* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
327.0ms	(+ (* (* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

simplify704.0ms

Counts

151 → 151

Iterations

Useful iterations: done (697.0ms)

Iter	Nodes	Cost
0	370	4022
1	1226	3516
done	5000	2840

prune809.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

regimes270.0ms

Accuracy

47.4% (3.8b remaining)

Error of 6.9b against oracle of 3.1b and baseline of 10.4b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	104
1	39	104
done	39	104

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s	7409×	body	80	valid
127.0ms	427×	body	640	valid
69.0ms	243×	body	1280	valid
66.0ms	383×	body	320	valid
30.0ms	257×	body	160	valid
3.0ms	9×	body	2560	valid