Details

sample34.0ms

Algorithm

intervals

Results

10.0ms	259×	body	80	valid
2.0ms	21×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	9×	body	1280	valid
1.0ms	10×	body	160	valid

simplify6.2s

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	322	12
5	766	12
6	1555	12
7	2873	12
8	4761	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.3b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite28.0ms

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:

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

series197.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- y z) (- a z))
142.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify1.1s

Counts

70 → 70

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	116	918
1	266	890
2	653	838
3	1707	834
done	5001	830

prune234.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
5.8b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite65.0ms

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:

15.0ms	(/ 1 (- a z))
46.0ms	(* (- y z) (/ 1 (- a z)))
0.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series233.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ 1 (- a z))
55.0ms	(* (- y z) (/ 1 (- a z)))
135.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify1.8s

Counts

114 → 114

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	152	1285
1	334	1052
2	930	948
3	3159	944
done	5002	942

prune310.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.3b	(fma (pow (/ (- y z) (- a z)) 1) (- t x) x)

rewrite27.0ms

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:

24.0ms	(/ (- y z) (- a z))
0.0ms	(fma (pow (/ (- y z) (- a z)) 1) (- t x) x)

series198.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- y z) (- a z))
139.0ms	(fma (pow (/ (- y z) (- a z)) 1) (- t x) x)

simplify1.1s

Counts

70 → 70

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	117	944
1	269	890
2	686	838
3	1923	834
done	5000	832

prune250.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1 (- a z)))
0.5b	(cbrt (/ 1 (- a z)))
0.5b	(* (cbrt (/ 1 (- a z))) (cbrt (/ 1 (- a z))))
11.1b	(fma (* (* (- y z) (* (cbrt (/ 1 (- a z))) (cbrt (/ 1 (- a z))))) (cbrt (/ 1 (- a z)))) (- t x) x)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

166×	`cbrt-prod`
142×	`add-sqr-sqrt`
130×	`*-un-lft-identity`
118×	`times-frac`
66×	`add-cube-cbrt`
32×	`swap-sqr`
24×	`associate-r` `associate-l` `distribute-lft-out--`
18×	`difference-of-squares`
16×	`unswap-sqr`
12×	`associate-/r/`
11×	`pow1`
8×	`pow1/3` `div-inv`
6×	`add-exp-log` `cbrt-div` `flip3--` `flip--`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 193

Calls

4 calls:

6.0ms	(cbrt (/ 1 (- a z)))
6.0ms	(cbrt (/ 1 (- a z)))
65.0ms	(* (cbrt (/ 1 (- a z))) (cbrt (/ 1 (- a z))))
0.0ms	(fma (* (* (- y z) (* (cbrt (/ 1 (- a z))) (cbrt (/ 1 (- a z))))) (cbrt (/ 1 (- a z)))) (- t x) x)

series629.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt (/ 1 (- a z)))
163.0ms	(cbrt (/ 1 (- a z)))
146.0ms	(* (cbrt (/ 1 (- a z))) (cbrt (/ 1 (- a z))))
143.0ms	(fma (* (* (- y z) (* (cbrt (/ 1 (- a z))) (cbrt (/ 1 (- a z))))) (cbrt (/ 1 (- a z)))) (- t x) x)

simplify1.6s

Counts

205 → 205

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	256	3859
1	453	3343
2	1001	3215
3	2437	2875
done	5000	2805

prune605.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 5.5b

regimes489.0ms

Accuracy

41.8% (4.8b remaining)

Error of 8.1b against oracle of 3.3b and baseline of 11.6b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	69
1	32	54
done	32	54

end0.0ms

sample792.0ms

Algorithm

intervals

Results

249.0ms	7805×	body	80	valid
58.0ms	497×	body	640	valid
37.0ms	268×	body	1280	valid
32.0ms	376×	body	320	valid
16.0ms	276×	body	160	valid
3.0ms	16×	body	2560	valid