Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
1.0ms	9×	body	1280	valid
1.0ms	11×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	45	12
3	122	12
4	303	12
5	741	12
6	1650	12
7	3370	12
done	5000	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.9b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite14.0ms

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:

11.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series136.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- t x) (- a z))
84.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify864.0ms

Counts

70 → 70

Iterations

Useful iterations: done (862.0ms)

Iter	Nodes	Cost
0	118	918
1	269	890
2	701	838
3	2280	834
done	5001	832

prune210.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
13.9b	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

11.0ms	(/ (- a z) (- t x))
13.0ms	(/ 1 (/ (- a z) (- t x)))
0.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series361.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- a z) (- t x))
190.0ms	(/ 1 (/ (- a z) (- t x)))
120.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify1.4s

Counts

223 → 223

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	274	3778
1	645	3362
2	2208	2943
done	5000	2931

prune389.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
4.5b	(+ (/ (- y z) (/ (- a z) (- t x))) x)
6.2b	(/ (- y z) (/ (- a z) (- t x)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
572×	`*-un-lft-identity`
570×	`add-sqr-sqrt`
200×	`add-cube-cbrt`
185×	`distribute-lft-out--` `difference-of-squares`
160×	`fma-def`
36×	`associate-/r*`
26×	`associate-/r/`
14×	`flip3--` `flip--` `div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

11.0ms	(/ (- a z) (- t x))
128.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
23.0ms	(/ (- y z) (/ (- a z) (- t x)))

series515.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- a z) (- t x))
165.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
299.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify1.0s

Counts

449 → 449

Iterations

Useful iterations: 2 (293.0ms)

Iter	Nodes	Cost
0	358	6030
1	1033	5673
2	4070	5522
done	5001	5522

prune1.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.8b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite14.0ms

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:

11.0ms	(/ (- y z) (- a z))
0.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series160.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- y z) (- a z))
110.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify834.0ms

Counts

70 → 70

Iterations

Useful iterations: done (832.0ms)

Iter	Nodes	Cost
0	116	918
1	266	890
2	705	838
3	2259	834
done	5000	832

prune168.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 3.2b

regimes392.0ms

Accuracy

6% (7.6b remaining)

Error of 11.2b against oracle of 3.6b and baseline of 11.6b

bsearch81.0ms

Steps

Iters	Range		Point
9	7.391227298622031e+270	1.4292821170447641e+277	9.257514045851647e+270
6	4.4620128093752744e-05	0.0005333266348582408	4.548562105535342e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	54
1	30	54
done	30	54

end0.0ms

sample701.0ms

Algorithm

intervals

Results

258.0ms	7756×	body	80	valid
64.0ms	492×	body	640	valid
41.0ms	278×	body	1280	valid
35.0ms	393×	body	320	valid
16.0ms	263×	body	160	valid
4.0ms	19×	body	2560	valid