Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	244×	body	80	valid
4.0ms	8×	body	1280	valid
2.0ms	18×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify5.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (12.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	114	12
4	278	12
5	614	12
6	1250	12
7	2321	12
8	4127	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.5b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite16.0ms

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

series186.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- y z) (- a z))
133.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	116	918
1	266	890
2	623	838
3	1565	834
4	4603	828
done	5000	828

prune223.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
4.5b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite35.0ms

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

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (- a z))
25.0ms	(* (- y z) (/ 1 (- a z)))
0.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series224.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (- a z))
53.0ms	(* (- y z) (/ 1 (- a z)))
130.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify2.4s

Counts

114 → 114

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	152	1285
1	341	1052
2	924	948
3	3049	944
done	5001	943

prune275.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.5b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
2.9b	(* (/ (- y z) (- a z)) (- t x))

rewrite77.0ms

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:

13.0ms	(/ (- y z) (- a z))
15.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
37.0ms	(* (/ (- y z) (- a z)) (- t x))

series578.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- y z) (- a z))
189.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
334.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify1.2s

Counts

179 → 179

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	255	3085
1	674	2718
2	2112	2494
done	5000	2458

prune451.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.0b	(/ (- y z) (- a z))
2.2b	(* (/ (- y z) (- a z)) t)
3.9b	(fma (/ (- y z) (- a z)) (- x) x)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
76×	`times-frac`
40×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-l`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r` `associate-/l`
6×	`pow1` `associate-/r/`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`frac-2neg` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 170

Calls

4 calls:

12.0ms	(/ (- y z) (- a z))
12.0ms	(/ (- y z) (- a z))
26.0ms	(* (/ (- y z) (- a z)) t)
0.0ms	(fma (/ (- y z) (- a z)) (- x) x)

series312.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (- y z) (- a z))
48.0ms	(/ (- y z) (- a z))
103.0ms	(* (/ (- y z) (- a z)) t)
106.0ms	(fma (/ (- y z) (- a z)) (- x) x)

simplify2.2s

Counts

182 → 182

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	162	2228
1	395	2164
2	1045	2030
3	3397	2030
done	5000	2015

prune536.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

regimes352.0ms

Accuracy

8.6% (4.3b remaining)

Error of 7.7b against oracle of 3.5b and baseline of 8.1b

bsearch76.0ms

Steps

Iters	Range		Point
5	1.1409411464878456e-174	4.551464151430799e-174	3.0988277645173375e-174
6	-1.609931513040364e-197	-2.951126666883304e-198	-4.787941776807318e-198

simplify5.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	27	83
1	34	52
done	34	52

end0.0ms

sample712.0ms

Algorithm

intervals

Results

272.0ms	7828×	body	80	valid
62.0ms	490×	body	640	valid
43.0ms	282×	body	1280	valid
37.0ms	401×	body	320	valid
15.0ms	242×	body	160	valid
3.0ms	18×	body	2560	valid