Details

sample67.0ms

Algorithm

intervals

Results

20.0ms	264×	body	80	valid
5.0ms	16×	body	640	valid
3.0ms	8×	body	1280	valid
2.0ms	7×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
12.7b	(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:

29.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series215.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(/ (- t x) (- a z))
122.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.8s

Counts

70 → 70

Iterations

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

prune576.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (- a z))
0.0b	(/ t (- a z))
0.3b	(- (/ t (- a z)) (/ x (- a z)))
12.7b	(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
693×	`times-frac`
441×	`prod-diff`
413×	`add-cube-cbrt`
149×	`distribute-lft-out--`
143×	`difference-of-squares`
94×	`associate-/r/`
48×	`flip3--` `flip--`
47×	`div-inv`
21×	`fma-neg`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`distribute-rgt-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `diff-log` `frac-sub` `fma-udef` `sub-div`

Counts

4 → 581

Calls

4 calls:

10.0ms	(/ x (- a z))
14.0ms	(/ t (- a z))
120.0ms	(- (/ t (- a z)) (/ x (- a z)))
0.0ms	(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

series378.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (- a z))
36.0ms	(/ t (- a z))
147.0ms	(- (/ t (- a z)) (/ x (- a z)))
136.0ms	(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

simplify1.8s

Counts

593 → 593

Iterations

Iter	Nodes
done	5000
2	3762
1	1285
0	574

prune3.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (- a z))
0.2b	(* x (/ 1 (- a z)))
0.3b	(- (/ t (- a z)) (* x (/ 1 (- a z))))
12.7b	(fma (- (/ t (- a z)) (* x (/ 1 (- a z)))) (- y z) x)

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
62×	`times-frac`
42×	`add-cube-cbrt`
21×	`fma-neg` `associate-r` `prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--` `difference-of-squares`
11×	`add-cbrt-cube`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
5×	`associate-/r*` `flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`div-exp` `associate-l` `associate-r/` `un-div-inv` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-sub` `cbrt-unprod` `sub-div`
1×	`rec-exp` `clear-num` `sub-neg` `frac-2neg` `distribute-rgt-out--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 156

Calls

4 calls:

10.0ms	(/ t (- a z))
29.0ms	(* x (/ 1 (- a z)))
90.0ms	(- (/ t (- a z)) (* x (/ 1 (- a z))))
1.0ms	(fma (- (/ t (- a z)) (* x (/ 1 (- a z)))) (- y z) x)

series410.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ t (- a z))
44.0ms	(* x (/ 1 (- a z)))
159.0ms	(- (/ t (- a z)) (* x (/ 1 (- a z))))
168.0ms	(fma (- (/ t (- a z)) (* x (/ 1 (- a z)))) (- y z) x)

simplify1.3s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	1834
1	526
0	216

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`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` `fma-def` `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` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

42.0ms	(/ (- t x) (- a z))
9.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
71.0ms	(* (- y z) (/ (- t x) (- a z)))

series484.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (- t x) (- a z))
215.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
187.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify2.2s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	2719
1	515
0	189

prune697.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.9b

regimes706.0ms

Accuracy

19.8% (7.2b remaining)

Error of 10.8b against oracle of 3.7b and baseline of 12.6b

bsearch155.0ms

Steps

Iters	Range		Point
5	9.657462100703732e-164	2.2403175115732038e-163	1.6831450817751837e-163
8	-7.039674671700918e-71	-6.993920488520829e-74	-1.978277154611088e-73

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	31

end0.0ms

sample1.6s

Algorithm

intervals

Results

630.0ms	7739×	body	80	valid
166.0ms	473×	body	640	valid
81.0ms	283×	body	1280	valid
68.0ms	412×	body	320	valid
47.0ms	270×	body	160	valid
6.0ms	17×	body	2560	valid