Details

sample40.0ms

Algorithm

intervals

Results

11.0ms	250×	body	80	valid
3.0ms	16×	body	1280	valid
2.0ms	15×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3818
5	978
4	326
3	116
2	45
1	20
0	11

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize38.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.4b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite45.0ms

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-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

40.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series244.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- y z) (- a z))
171.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify1.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4622
2	860
1	271
0	116

prune499.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.9b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
1.4b	(+ (/ (- t x) (/ (- a z) (- y z))) x)
2.4b	(/ (- t x) (/ (- a z) (- y z)))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
572×	`*-un-lft-identity`
570×	`add-sqr-sqrt`
200×	`add-cube-cbrt`
185×	`distribute-lft-out--` `difference-of-squares`
160×	`fma-def`
36×	`associate-/r*`
26×	`associate-/r/`
14×	`flip3--` `div-inv` `flip--`
10×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3-+` `associate-+l-` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

28.0ms	(/ (- a z) (- y z))
264.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
40.0ms	(/ (- t x) (/ (- a z) (- y z)))

series744.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ (- a z) (- y z))
299.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
345.0ms	(/ (- t x) (/ (- a z) (- y z)))

simplify638.0ms

Counts

449 → 449

Iterations

Iter	Nodes
done	5001
1	1165
0	360

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
3.6b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite73.0ms

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-/r` `associate-l*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 105

Calls

3 calls:

16.0ms	(/ 1 (- a z))
51.0ms	(* (- y z) (/ 1 (- a z)))
0.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series377.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ 1 (- a z))
105.0ms	(* (- y z) (/ 1 (- a z)))
215.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify4.1s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2819
1	363
0	152

prune753.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

localize48.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
2.1b	(/ t (/ (- a z) (- y z)))
24.3b	(fma (/ x (- a z)) (- y z) (- x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
11×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/l*`
6×	`flip3--` `div-inv` `flip--`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`div-sub` `fma-udef`

Counts

3 → 208

Calls

3 calls:

28.0ms	(/ (- a z) (- y z))
21.0ms	(/ t (/ (- a z) (- y z)))
0.0ms	(fma (/ x (- a z)) (- y z) (- x))

series494.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- a z) (- y z))
257.0ms	(/ t (/ (- a z) (- y z)))
156.0ms	(fma (/ x (- a z)) (- y z) (- x))

simplify1.5s

Counts

217 → 217

Iterations

Iter	Nodes
done	5000
2	3921
1	768
0	291

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

regimes881.0ms

Accuracy

17.2% (6.6b remaining)

Error of 10.1b against oracle of 3.4b and baseline of 11.4b

bsearch165.0ms

Steps

Iters	Range		Point
10	2.1039460058121797e-189	5.334963794456662e-178	2.5556154591904095e-179
6	-8.18404917531175e-49	-9.569740050098368e-50	-9.775356164441544e-50

simplify7.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	7893×	body	80	valid
132.0ms	428×	body	640	valid
95.0ms	322×	body	1280	valid
94.0ms	376×	body	320	valid
31.0ms	260×	body	160	valid
7.0ms	19×	body	2560	valid