Details

sample73.0ms

Algorithm

intervals

Results

30.0ms	237×	body	80	valid
4.0ms	20×	body	320	valid
3.0ms	12×	body	640	valid
3.0ms	7×	body	1280	valid
1.0ms	5×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 4 (62.0ms)

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite54.0ms

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:

48.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series371.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ (- t z) (- a t))
290.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.9s

Counts

70 → 70

Iterations

Useful iterations: 3 (979.0ms)

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

prune517.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.4b	(* (/ (- t z) (- a t)) y)
2.5b	(+ (* (/ (- t z) (- a t)) y) (+ x y))

rewrite165.0ms

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:

26.0ms	(/ (- t z) (- a t))
59.0ms	(* (/ (- t z) (- a t)) y)
73.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

series603.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (- t z) (- a t))
188.0ms	(* (/ (- t z) (- a t)) y)
351.0ms	(+ (* (/ (- 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

prune841.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t z))
0.7b	(* (/ (cbrt (- t z)) (- a t)) y)
5.4b	(* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt (- t z)) (- a t)) y))
8.5b	(+ (* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt (- t z)) (- a t)) y)) (+ x y))

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-exp-log`
63×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
53×	`associate-l`
45×	`times-frac`
35×	`add-cbrt-cube`
33×	`prod-exp`
31×	`cbrt-prod`
27×	`add-cube-cbrt`
20×	`cbrt-unprod`
18×	`div-exp`
14×	`distribute-lft-out--` `difference-of-squares`
11×	`pow1`
10×	`cbrt-undiv` `associate-*l/`
9×	`add-log-exp`
6×	`1-exp` `frac-add`
4×	`expm1-log1p-u` `flip3-+` `associate-r` `pow-prod-down` `flip-+` `log1p-expm1-u`
3×	`frac-times` `associate-*r/` `sum-log` `unswap-sqr`
2×	`cbrt-div` `flip3--` `associate-/r/` `*-commutative` `flip--` `div-inv`
1×	`+-commutative` `associate-+r+` `fma-def` `pow1/3`

Counts

4 → 154

Calls

4 calls:

4.0ms	(cbrt (- t z))
66.0ms	(* (/ (cbrt (- t z)) (- a t)) y)
136.0ms	(* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt (- t z)) (- a t)) y))
188.0ms	(+ (* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt (- t z)) (- a t)) y)) (+ x y))

series1.7s

Counts

4 → 12

Calls

4 calls:

241.0ms	(cbrt (- t z))
954.0ms	(* (/ (cbrt (- t z)) (- a t)) y)
143.0ms	(* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt (- t z)) (- a t)) y))
324.0ms	(+ (* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt (- t z)) (- a t)) y)) (+ x y))

simplify606.0ms

Counts

166 → 166

Iterations

Useful iterations: done (601.0ms)

Iter	Nodes	Cost
0	301	3397
1	908	3013
done	5001	2633

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t z))
0.6b	(cbrt (- t z))
4.9b	(+ (* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt 1) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- t z)) (cbrt (- a t))) y))) (+ x y))
5.4b	(* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt 1) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- t z)) (cbrt (- a t))) y)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

279×	`add-exp-log`
160×	`prod-exp`
101×	`add-cbrt-cube`
94×	`cbrt-unprod`
85×	`div-exp`
47×	`cbrt-undiv`
21×	`associate-*l/`
20×	`1-exp`
15×	`frac-times` `associate-*r/`
14×	`frac-add`
13×	`pow1`
12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
9×	`add-log-exp`
8×	`add-cube-cbrt` `flip3-+` `flip-+`
7×	`associate-l`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `cbrt-div` `log1p-expm1-u`
3×	`times-frac` `sum-log`
2×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `fma-def` `associate-r` `*-commutative` `div-inv`

Counts

4 → 172

Calls

4 calls:

4.0ms	(cbrt (- t z))
4.0ms	(cbrt (- t z))
519.0ms	(+ (* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt 1) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- t z)) (cbrt (- a t))) y))) (+ x y))
611.0ms	(* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt 1) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- t z)) (cbrt (- a t))) y)))

series1.0s

Counts

4 → 12

Calls

4 calls:

238.0ms	(cbrt (- t z))
268.0ms	(cbrt (- t z))
343.0ms	(+ (* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt 1) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- t z)) (cbrt (- a t))) y))) (+ x y))
176.0ms	(* (/ (* (cbrt (- t z)) (cbrt (- t z))) 1) (* (/ (cbrt 1) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- t z)) (cbrt (- a t))) y)))

simplify1.0s

Counts

184 → 184

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	365	7935
1	1408	6772
done	5000	5036

prune921.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.6b

regimes732.0ms

Accuracy

34.1% (5.5b remaining)

Error of 8.7b against oracle of 3.2b and baseline of 11.5b

bsearch123.0ms

Steps

Iters	Range		Point
5	3.198071978483055e+143	1.172557482531829e+144	3.7093152088217044e+143
9	-6.432413953408245e+56	-3.530949691192172e+50	-4.762781964643517e+56

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	28	59
1	36	51
done	36	51

end0.0ms

sample1.8s

Algorithm

intervals

Results

568.0ms	7374×	body	80	valid
434.0ms	402×	body	320	valid
187.0ms	455×	body	640	valid
64.0ms	241×	body	1280	valid
29.0ms	269×	body	160	valid
2.0ms	7×	body	2560	valid