Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	259×	body	80	valid
3.0ms	13×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	4×	body	1280	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (16.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	326	12
5	1014	12
6	4061	12
done	5000	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.8b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite48.0ms

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:

45.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series253.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(/ (- y z) (- a z))
168.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify2.7s

Counts

70 → 70

Iterations

Useful iterations: 3 (892.0ms)

Iter	Nodes	Cost
0	116	918
1	271	890
2	855	840
3	4496	834
done	5000	834

prune343.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.8b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.2b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
2.5b	(* (/ (- y z) (- a z)) (- t x))

rewrite172.0ms

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:

41.0ms	(/ (- y z) (- a z))
32.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
88.0ms	(* (/ (- y z) (- a z)) (- t x))

series858.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- y z) (- a z))
278.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
501.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify2.0s

Counts

179 → 179

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	255	3085
1	716	2731
2	3223	2500
done	5000	2468

prune779.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
4.3b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite97.0ms

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:

25.0ms	(/ 1 (- a z))
68.0ms	(* (- y z) (/ 1 (- a z)))
1.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series321.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ 1 (- a z))
86.0ms	(* (- y z) (/ 1 (- a z)))
181.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify6.7s

Counts

114 → 114

Iterations

Useful iterations: done (6.7s)

Iter	Nodes	Cost
0	152	1285
1	363	1135
2	2806	954
done	5000	948

prune461.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(* (cbrt (- y z)) (cbrt (- y z)))
2.5b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x))
6.9b	(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x)) x)

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

114×	`add-sqr-sqrt`
102×	`*-un-lft-identity`
91×	`times-frac`
59×	`cbrt-prod` `associate-l`
58×	`add-cube-cbrt`
36×	`prod-diff`
24×	`add-exp-log`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
16×	`cbrt-div` `add-cbrt-cube`
13×	`pow1` `associate-r`
10×	`flip3--` `swap-sqr` `flip--`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
7×	`pow1/3`
6×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u`
3×	`pow-prod-down` `associate-*l/` `associate-/r/`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `fma-def` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 219

Calls

4 calls:

4.0ms	(cbrt (- y z))
54.0ms	(* (cbrt (- y z)) (cbrt (- y z)))
207.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x))
114.0ms	(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x)) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt (- y z))
266.0ms	(* (cbrt (- y z)) (cbrt (- y z)))
552.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x))
323.0ms	(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x)) x)

simplify913.0ms

Counts

231 → 231

Iterations

Useful iterations: done (895.0ms)

Iter	Nodes	Cost
0	385	5567
1	1081	5101
done	5000	4694

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

regimes399.0ms

Accuracy

13.9% (7.4b remaining)

Error of 10.8b against oracle of 3.4b and baseline of 11.9b

bsearch187.0ms

Steps

Iters	Range		Point
9	2.178955092501884e-123	3.9054077061397985e-118	2.8263443798943843e-123
9	-4.8657234938157416e-248	-5.0957024340937645e-256	-4.773373498705184e-248

simplify7.0ms

Iterations

Useful iterations: done (7.0ms)

Iter	Nodes	Cost
0	32	63
1	39	60
done	39	58

end0.0ms

sample1.7s

Algorithm

intervals

Results

675.0ms	7771×	body	80	valid
219.0ms	486×	body	640	valid
109.0ms	422×	body	320	valid
65.0ms	251×	body	1280	valid
30.0ms	284×	body	160	valid
5.0ms	11×	body	2560	valid