Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	238×	body	80	valid
2.0ms	12×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	8×	body	640	valid
1.0ms	10×	body	160	valid

simplify8.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (31.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	51	13
3	103	13
4	205	12
5	408	12
6	672	12
7	935	12
8	1113	12
9	1379	12
10	1828	12
11	2805	12
12	3999	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.0b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite15.0ms

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:

12.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series237.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- t z) (- a t))
190.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	113	906
1	258	878
2	589	826
3	1517	824
4	4609	822
done	5000	822

prune237.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t z))
0.6b	(cbrt (- t z))
0.6b	(cbrt (- t z))
7.4b	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y (+ x y))

rewrite12.0ms

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:

2.0ms	(cbrt (- t z))
2.0ms	(cbrt (- t z))
3.0ms	(cbrt (- t z))
3.0ms	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y (+ x y))

series686.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (- t z))
168.0ms	(cbrt (- t z))
165.0ms	(cbrt (- t z))
197.0ms	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y (+ x y))

simplify1.7s

Counts

73 → 73

Iterations

Useful iterations: 4 (712.0ms)

Iter	Nodes	Cost
0	93	913
1	192	895
2	409	737
3	1030	666
4	3846	630
done	5001	630

prune317.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.2b	(* y (/ (- t z) (- a t)))
2.3b	(+ (* y (/ (- t z) (- a t))) (+ x y))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
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:

16.0ms	(/ (- t z) (- a t))
26.0ms	(* y (/ (- t z) (- a t)))
15.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))

series267.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- t z) (- a t))
74.0ms	(* y (/ (- t z) (- a t)))
147.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))

simplify755.0ms

Counts

133 → 133

Iterations

Useful iterations: done (751.0ms)

Iter	Nodes	Cost
0	190	1752
1	530	1625
2	1562	1541
done	5001	1533

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
5.1b	(* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t))))
6.4b	(+ (* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) (+ x y))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
50×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
23×	`associate-l`
20×	`distribute-lft-out--`
18×	`add-cbrt-cube` `difference-of-squares`
14×	`flip3--` `flip--`
13×	`pow1`
11×	`frac-times`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`cbrt-undiv` `pow1/3` `associate-r/` `div-exp` `associate-l/`
6×	`frac-add`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-prod-down` `sum-log`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `associate-+r+` `fma-def` `pow-plus`

Counts

4 → 190

Calls

4 calls:

2.0ms	(cbrt (- a t))
21.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
76.0ms	(* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t))))
45.0ms	(+ (* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) (+ x y))

series589.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (- a t))
145.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
166.0ms	(* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t))))
110.0ms	(+ (* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) (+ x y))

simplify1.9s

Counts

202 → 202

Iterations

Useful iterations: 2 (928.0ms)

Iter	Nodes	Cost
0	346	4259
1	1025	3944
2	4225	3355
done	5000	3355

prune703.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.6b

regimes348.0ms

Accuracy

40.2% (4.6b remaining)

Error of 8.1b against oracle of 3.4b and baseline of 11.2b

bsearch84.0ms

Steps

Iters	Range		Point
6	4.561674216475071e+93	2.1094233064695275e+94	5.622875397189695e+93
7	-4.3267794471986547e+120	-1.3361566680160774e+119	-1.4785650511945879e+119

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	51
1	32	46
done	32	46

end0.0ms

sample656.0ms

Algorithm

intervals

Results

242.0ms	7324×	body	80	valid
56.0ms	484×	body	640	valid
44.0ms	257×	body	1280	valid
40.0ms	413×	body	320	valid
14.0ms	234×	body	160	valid
2.0ms	11×	body	2560	valid