Details

sample64.0ms

Algorithm

intervals

Results

13.0ms	192×	body	80	valid
13.0ms	31×	body	2560	valid
6.0ms	18×	body	1280	valid
6.0ms	256×	pre	80	true
2.0ms	7×	body	640	valid
2.0ms	4×	body	5120	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify112.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	40	16
3	47	16
4	49	16
5	51	16
6	52	16
done	52	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite185.0ms

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:

17.0ms	(+ (* (* 4.0 p) p) (* x x))
52.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
32.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (* (* 4.0 p) p) (* x x))
84.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
100.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.9s

Counts

103 → 103

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	136	1755
1	294	1489
2	840	1391
3	2363	1379
done	5000	1375

prune529.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2)))))
8.2b	(+ 1.0 (* (/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) (/ x (sqrt (cbrt (fma 4.0 (pow p 2) (pow x 2)))))))
14.9b	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
14.9b	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

5.0ms	(/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2)))))
6.0ms	(+ 1.0 (* (/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) (/ x (sqrt (cbrt (fma 4.0 (pow p 2) (pow x 2)))))))
1.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2)))))
326.0ms	(+ 1.0 (* (/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) (/ x (sqrt (cbrt (fma 4.0 (pow p 2) (pow x 2)))))))
206.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))
189.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

simplify2.1s

Counts

87 → 87

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	147	1756
1	319	1661
2	841	1471
3	2644	1450
done	5000	1439

prune536.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize41.0ms

Local error

Found 4 expressions with local error:

7.7b	(+ 1.0 (* (/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) (/ x (sqrt (* (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))))
14.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
14.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
14.9b	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

6.0ms	(+ 1.0 (* (/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) (/ x (sqrt (* (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
3.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

402.0ms	(+ 1.0 (* (/ 1 (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) (/ x (sqrt (* (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))))
82.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
83.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
174.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

simplify1.9s

Counts

71 → 71

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	117	1516
1	275	1205
2	790	1071
3	2528	1058
done	5001	1040

prune726.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))
5.6b	(+ (/ (/ x (fabs (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))) (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) 1.0)
14.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
14.9b	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
45×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `fma-def`
9×	`cbrt-prod`
6×	`sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
2×	`pow1/3`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

3.0ms	(cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))
75.0ms	(+ (/ (/ x (fabs (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))) (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) 1.0)
3.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))
96.0ms	(+ (/ (/ x (fabs (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))) (fabs (cbrt (fma 4.0 (pow p 2) (pow x 2))))) 1.0)
99.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
200.0ms	(cbrt (fma 4.0 (pow p 2) (pow x 2)))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	127	1372
1	264	1321
2	627	1210
3	1665	1162
done	5001	1154

prune929.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.1b

regimes420.0ms

Accuracy

87.3% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 14.8b

bsearch110.0ms

Steps

Iters	Range		Point
7	-7.743494490041011e-139	-1.924856853462337e-140	-6.891572154331307e-140

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	70
1	39	70
done	39	70

end0.0ms

sample2.2s

Algorithm

intervals

Results

933.0ms	6070×	body	80	valid
346.0ms	739×	body	2560	valid
248.0ms	594×	body	1280	valid
152.0ms	8000×	pre	80	true
111.0ms	311×	body	640	valid
28.0ms	58×	body	5120	valid
27.0ms	156×	body	320	valid
8.0ms	72×	body	160	valid