Details

sample56.0ms

Algorithm

intervals

Results

23.0ms	242×	body	80	valid
5.0ms	20×	body	640	valid
3.0ms	12×	body	1280	valid
3.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 3 (15.0ms)

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: 13.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.5b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite43.0ms

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:

37.0ms	(/ (- y z) (- a z))
0.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series293.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- y z) (- a z))
226.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify2.6s

Counts

70 → 70

Iterations

Useful iterations: 3 (859.0ms)

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

prune302.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.0b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
2.2b	(* (/ (- y z) (- a z)) (- t x))

rewrite226.0ms

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:

56.0ms	(/ (- y z) (- a z))
38.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
116.0ms	(* (/ (- y z) (- a z)) (- t x))

series944.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(/ (- y z) (- a z))
284.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
552.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify1.8s

Counts

179 → 179

Iterations

Useful iterations: done (1.8s)

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

prune714.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.0b	(/ (- y z) (- a z))
1.8b	(* (/ (- y z) (- a z)) t)
2.4b	(fma (/ (- y z) (- a z)) (- x) x)

rewrite189.0ms

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:

38.0ms	(/ (- y z) (- a z))
41.0ms	(/ (- y z) (- a z))
95.0ms	(* (/ (- y z) (- a z)) t)
1.0ms	(fma (/ (- y z) (- a z)) (- x) x)

series582.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- y z) (- a z))
103.0ms	(/ (- y z) (- a z))
214.0ms	(* (/ (- y z) (- a z)) t)
177.0ms	(fma (/ (- y z) (- a z)) (- x) x)

simplify1.2s

Counts

182 → 182

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	162	2228
1	406	2164
2	1563	2038
done	5000	2030

prune811.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.8b	(* (* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t))) (cbrt t))
1.3b	(* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t)))
2.4b	(fma (/ (- y z) (- a z)) (- x) x)

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
34×	`add-exp-log`
32×	`associate-l`
26×	`times-frac`
21×	`add-cbrt-cube`
18×	`pow1` `add-cube-cbrt`
17×	`prod-exp` `cbrt-unprod`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow-prod-down`
7×	`associate-r`
6×	`cbrt-prod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/`
2×	`associate-/r/` `*-commutative` `unswap-sqr`
1×	`flip3--` `pow1/3` `flip--` `fma-udef` `div-inv`

Counts

4 → 109

Calls

4 calls:

1.0ms	(cbrt t)
180.0ms	(* (* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t))) (cbrt t))
105.0ms	(* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t)))
1.0ms	(fma (/ (- y z) (- a z)) (- x) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

319.0ms	(cbrt t)
231.0ms	(* (* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t))) (cbrt t))
338.0ms	(* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t)))
142.0ms	(fma (/ (- y z) (- a z)) (- x) x)

simplify1.8s

Counts

121 → 121

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	166	1807
1	464	1774
2	2290	1308
done	5000	1217

prune619.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.3b

regimes526.0ms

Accuracy

6.2% (4.7b remaining)

Error of 8.3b against oracle of 3.5b and baseline of 8.6b

bsearch163.0ms

Steps

Iters	Range		Point
9	3.5912154120747196e-109	1.1702822108249084e-100	1.0793466330024646e-104
6	-2.1564359723426472e-113	-1.3751529682407275e-114	-2.384298577098447e-114

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	97
1	38	61
done	38	61

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	7771×	body	80	valid
200.0ms	462×	body	640	valid
101.0ms	321×	body	1280	valid
83.0ms	414×	body	320	valid
68.0ms	252×	body	160	valid
6.0ms	15×	body	2560	valid