Details

sample32.0ms

Algorithm

intervals

Results

7.0ms	199×	body	80	valid
5.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	18×	body	1280	valid
2.0ms	11×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	39	16
3	46	16
4	48	16
5	50	16
6	51	16
done	51	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

15.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
7.0ms	(+ (* (* 4.0 p) p) (* x x))
27.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
37.0ms	(+ (* (* 4.0 p) p) (* x x))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: 3 (517.0ms)

Iter	Nodes	Cost
0	136	1755
1	296	1489
2	854	1391
3	2981	1379
done	5000	1379

prune384.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))))
0.6b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
4.0b	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
13.5b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`log-prod`
7×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `exp-prod` `exp-sum` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `distribute-lft-out`
2×	`exp-diff` `log-pow`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `rem-exp-log`

Counts

4 → 69

Calls

4 calls:

10.0ms	(exp (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))))
10.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
10.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(exp (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))))
79.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
180.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
59.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify1.9s

Counts

81 → 81

Iterations

Useful iterations: 5 (1.0s)

Iter	Nodes	Cost
0	103	1383
1	189	1264
2	358	1129
3	718	1095
4	1686	1086
5	4541	1084
done	5000	1084

prune313.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))) 3)
0.6b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
4.0b	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
13.5b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`pow1`
6×	`add-exp-log` `add-log-exp`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `unpow-prod-down` `log-prod` `cube-prod` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `sqrt-prod` `log-pow`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

2.0ms	(pow (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))) 3)
9.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
9.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

series698.0ms

Counts

4 → 12

Calls

4 calls:

382.0ms	(pow (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))) 3)
77.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
180.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
60.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify1.4s

Counts

88 → 88

Iterations

Useful iterations: 3 (354.0ms)

Iter	Nodes	Cost
0	110	1573
1	242	1433
2	606	1303
3	2587	1279
done	5000	1279

prune379.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))) 3)
0.6b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
4.0b	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
13.5b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`pow1`
6×	`add-exp-log` `add-log-exp`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `unpow-prod-down` `log-prod` `cube-prod` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `sqrt-prod` `log-pow`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

2.0ms	(pow (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))) 3)
9.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
9.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

series698.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(pow (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))) 3)
77.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
181.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
61.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify1.6s

Counts

88 → 88

Iterations

Useful iterations: 3 (350.0ms)

Iter	Nodes	Cost
0	110	1573
1	242	1433
2	606	1303
3	2587	1279
done	5000	1279

prune359.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.0b

regimes121.0ms

Accuracy

0% (3.7b remaining)

Error of 13.3b against oracle of 9.6b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	27
1	25	27
done	25	27

end0.0ms

sample815.0ms

Algorithm

intervals

Results

208.0ms	6026×	body	80	valid
178.0ms	809×	body	2560	valid
106.0ms	597×	body	1280	valid
106.0ms	8000×	pre	80	true
43.0ms	317×	body	640	valid
17.0ms	166×	body	320	valid
6.0ms	85×	body	160	valid