Details

sample44.0ms

Algorithm

intervals

Results

18.0ms	242×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	4×	body	1280	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify6.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	46	12
3	128	12
4	360	12
5	877	12
6	2016	12
7	3586	12
done	5000	12

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.7b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite62.0ms

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:

56.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series208.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ (- t x) (- a z))
148.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.4s

Counts

70 → 70

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	118	918
1	269	890
2	658	838
3	1743	834
done	5000	830

prune292.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.8b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.6b	(+ (* (/ (- t x) (- a z)) (- y z)) x)
5.4b	(* (/ (- t x) (- a z)) (- y z))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

26.0ms	(/ (- t x) (- a z))
31.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
130.0ms	(* (/ (- t x) (- a z)) (- y z))

series626.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (- t x) (- a z))
247.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
305.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify1.4s

Counts

179 → 179

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	256	3107
1	665	2740
2	1928	2516
done	5002	2490

prune653.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.9b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.3b	(+ (* (- t x) (/ (- y z) (- a z))) x)
2.4b	(* (- t x) (/ (- y z) (- a z)))

rewrite205.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

49.0ms	(/ (- y z) (- a z))
25.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
118.0ms	(* (- t x) (/ (- y z) (- a z)))

series489.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (- y z) (- a z))
239.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
182.0ms	(* (- t x) (/ (- y z) (- a z)))

simplify1.2s

Counts

135 → 135

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	189	1881
1	486	1765
2	1775	1669
done	5000	1667

prune513.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.3b	(/ 1 (/ (- a z) (- y z)))
2.3b	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)
2.4b	(* (- t x) (/ 1 (/ (- a z) (- y z))))

rewrite337.0ms

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×	`add-exp-log` `associate-/r*`
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` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `fma-def` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 353

Calls

4 calls:

39.0ms	(/ (- a z) (- y z))
27.0ms	(/ 1 (/ (- a z) (- y z)))
71.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)
177.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))

series814.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- a z) (- y z))
210.0ms	(/ 1 (/ (- a z) (- y z)))
223.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)
294.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))

simplify2.6s

Counts

365 → 365

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	403	6260
1	998	5130
2	2756	4711
done	5000	4633

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

regimes353.0ms

Accuracy

23% (6.4b remaining)

Error of 9.9b against oracle of 3.5b and baseline of 11.9b

bsearch196.0ms

Steps

Iters	Range		Point
11	1.270532878618462e-164	2.6487703454575654e-144	7.692781660197599e-150
8	-4.128450568952297e-153	-5.6397930640659014e-157	-4.566794582426087e-156

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	26	49
1	30	47
done	30	47

end0.0ms

sample1.7s

Algorithm

intervals

Results

706.0ms	7761×	body	80	valid
171.0ms	474×	body	640	valid
78.0ms	281×	body	1280	valid
74.0ms	432×	body	320	valid
30.0ms	274×	body	160	valid
5.0ms	15×	body	2560	valid