Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	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

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4619
5	1129
4	367
3	128
2	46
1	23
0	11

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.9b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.0b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite32.0ms

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:

27.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series247.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(/ (- t x) (- a z))
167.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.4s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4626
2	848
1	274
0	118

prune523.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.2b	(+ (* (/ (- t x) (- a z)) (- y z)) x)
3.8b	(* (/ (- t x) (- a z)) (- y z))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

37.0ms	(/ (- t x) (- a z))
45.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
105.0ms	(* (/ (- t x) (- a z)) (- y z))

series553.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ (- t x) (- a z))
221.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
262.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify1.3s

Counts

179 → 179

Iterations

Iter	Nodes
done	5001
2	3330
1	717
0	256

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.3b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.4b	(+ (* (- t x) (/ (- y z) (- a z))) x)
2.0b	(* (- t x) (/ (- y z) (- a z)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

30.0ms	(/ (- y z) (- a z))
26.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
70.0ms	(* (- t x) (/ (- y z) (- a z)))

series510.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (- y z) (- a z))
271.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
183.0ms	(* (- t x) (/ (- y z) (- a z)))

simplify1.5s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	2647
1	517
0	189

prune772.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.6b	(/ 1 (/ (- a z) (- y z)))
1.4b	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)
2.0b	(* (- t x) (/ 1 (/ (- a z) (- y z))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*` `add-exp-log`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/` `associate-/l/`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 353

Calls

4 calls:

23.0ms	(/ (- a z) (- y z))
40.0ms	(/ 1 (/ (- a z) (- y z)))
42.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)
129.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))

series793.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (- a z) (- y z))
174.0ms	(/ 1 (/ (- a z) (- y z)))
251.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)
310.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))

simplify705.0ms

Counts

365 → 365

Iterations

Iter	Nodes
done	5001
1	1180
0	403

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

regimes641.0ms

Accuracy

-1.3% (8.0b remaining)

Error of 11.4b against oracle of 3.5b and baseline of 11.3b

bsearch126.0ms

Steps

Iters	Range		Point
10	2.1039460058121797e-189	5.334963794456662e-178	9.245984676792925e-181
6	-2.4031652791127273e-20	-2.0990955826697636e-21	-2.1458694787615367e-21

simplify4.0ms

Iterations

Iter	Nodes
done	33
2	33
1	32
0	27

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	7893×	body	80	valid
126.0ms	322×	body	1280	valid
120.0ms	429×	body	640	valid
103.0ms	375×	body	320	valid
30.0ms	260×	body	160	valid
7.0ms	19×	body	2560	valid