Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	249×	body	80	valid
4.0ms	15×	body	640	valid
3.0ms	9×	body	1280	valid
1.0ms	6×	body	160	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	2560	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 4 (56.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.5b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite37.0ms

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:

34.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series353.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- t z) (- a t))
286.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.5s

Counts

70 → 70

Iterations

Useful iterations: 3 (982.0ms)

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

prune317.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.5b	(* (/ (- t z) (- a t)) y)
1.8b	(+ (* (/ (- t z) (- a t)) y) (+ x y))

rewrite167.0ms

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:

51.0ms	(/ (- t z) (- a t))
68.0ms	(* (/ (- t z) (- a t)) y)
33.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

series525.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (- t z) (- a t))
138.0ms	(* (/ (- t z) (- a t)) y)
299.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

simplify2.1s

Counts

133 → 133

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	195	1736
1	554	1646
2	2346	1560
done	5001	1558

prune538.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
3.5b	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

rewrite102.0ms

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:

13.0ms	(/ 1 (- a t))
84.0ms	(* (- t z) (/ 1 (- a t)))
1.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

series339.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ 1 (- a t))
57.0ms	(* (- t z) (/ 1 (- a t)))
235.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

simplify5.7s

Counts

114 → 114

Iterations

Useful iterations: done (5.7s)

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

prune353.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
7.4b	(fma (* (- t z) (/ (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))) y (+ x y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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:

6.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
0.0ms	(fma (* (- t z) (/ (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))) y (+ x y))

series1.3s

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt (- a t))
197.0ms	(cbrt (- a t))
220.0ms	(cbrt (- a t))
655.0ms	(fma (* (- t z) (/ (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))) y (+ x y))

simplify1.0s

Counts

73 → 73

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	95	939
1	192	921
2	483	759
3	1726	666
done	5002	630

prune336.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.7b

regimes372.0ms

Accuracy

31.1% (5.7b remaining)

Error of 9.1b against oracle of 3.4b and baseline of 11.7b

bsearch102.0ms

Steps

Iters	Range		Point
10	7.025783171338231e-125	3.277101662510517e-115	1.0183768916294837e-117
7	-6.159056418506535e-125	-6.637490052300637e-127	-8.757676766814286e-126

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	20	42
1	27	29
done	27	29

end0.0ms

sample1.5s

Algorithm

intervals

Results

561.0ms	7355×	body	80	valid
121.0ms	456×	body	640	valid
102.0ms	264×	body	1280	valid
62.0ms	417×	body	320	valid
56.0ms	255×	body	160	valid
4.0ms	14×	body	2560	valid