Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	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

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	284	12
5	650	12
6	1496	12
7	3171	12
8	4923	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

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)

rewrite19.0ms

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)

series165.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- y z) (- a z))
115.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify869.0ms

Counts

70 → 70

Iterations

Useful iterations: done (867.0ms)

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

prune216.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.6b

localize13.0ms

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)

rewrite34.0ms

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)

series205.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1 (- a z))
51.0ms	(* (- y z) (/ 1 (- a z)))
119.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify2.8s

Counts

114 → 114

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	152	1285
1	346	1096
2	1245	948
3	4332	944
done	5000	943

prune286.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.5b	(* (- t x) (/ (- y z) (- a z)))
3.5b	(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

12.0ms	(/ (- y z) (- a z))
35.0ms	(* (- t x) (/ (- y z) (- a z)))
12.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series332.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- y z) (- a z))
122.0ms	(* (- t x) (/ (- y z) (- a z)))
156.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify644.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (142.0ms)

Iter	Nodes	Cost
0	189	1881
1	493	1765
2	1911	1669
done	5000	1669

prune363.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.3b	(/ 1 (/ (- a z) (- y z)))
1.5b	(* (- t x) (/ 1 (/ (- a z) (- y z))))
3.5b	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `fma-def` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 353

Calls

4 calls:

13.0ms	(/ (- a z) (- y z))
15.0ms	(/ 1 (/ (- a z) (- y z)))
64.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))
18.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

series548.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (- a z) (- y z))
139.0ms	(/ 1 (/ (- a z) (- y z)))
208.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))
148.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

simplify2.1s

Counts

365 → 365

Iterations

Useful iterations: 2 (421.0ms)

Iter	Nodes	Cost
0	403	6260
1	1046	5412
2	3867	4711
done	5000	4711

prune788.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.2b

regimes299.0ms

Accuracy

23% (6.3b remaining)

Error of 9.7b against oracle of 3.4b and baseline of 11.6b

bsearch105.0ms

Steps

Iters	Range		Point
11	9.185867048517993e+224	1.1690037944292812e+247	1.1134789946894111e+226
7	-3.446334398642131e+240	-3.9515387378738594e+238	-9.191459456486792e+238

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	22	43
1	28	33
done	28	33

end0.0ms

sample688.0ms

Algorithm

intervals

Results

252.0ms	7755×	body	80	valid
64.0ms	492×	body	640	valid
41.0ms	277×	body	1280	valid
35.0ms	395×	body	320	valid
16.0ms	263×	body	160	valid
4.0ms	19×	body	2560	valid