Details

sample48.0ms

Algorithm

intervals

Results

13.0ms	26×	body	2560	valid
9.0ms	195×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	16×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	5×	body	640	valid
0.0ms	4×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize13.0ms

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))))
0.9b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite220.0ms

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:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
39.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
109.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
33.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* (* 4.0 p) p) (* x x))
60.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
104.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
83.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts

103 → 103

Iterations

Useful iterations: done (2.0s)

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

prune640.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
0.9b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
2.4b	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
14.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite60.0ms

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:

16.0ms	(exp (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
26.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
14.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series589.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(exp (log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
143.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
236.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
96.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify5.0s

Counts

81 → 81

Iterations

Useful iterations: 5 (3.6s)

Iter	Nodes	Cost
0	103	1383
1	191	1264
2	387	1129
3	773	1095
4	1922	1086
5	4883	1084
done	5000	1084

prune515.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize32.0ms

Local error

Found 4 expressions with local error:

2.4b	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3)) (fma (/ x (fma 4.0 (pow p 2) (pow x 2))) x (* (- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))) 1.0))))
2.7b	(/ x (fma 4.0 (pow p 2) (pow x 2)))
14.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
14.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
36×	`times-frac`
31×	`log-prod`
29×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
15×	`distribute-lft-out`
12×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log`
7×	`pow1`
6×	`sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `sum-cubes` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `div-inv`
1×	`cbrt-undiv` `log-div` `frac-2neg` `clear-num` `log-pow`

Counts

4 → 103

Calls

4 calls:

97.0ms	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3)) (fma (/ x (fma 4.0 (pow p 2) (pow x 2))) x (* (- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))) 1.0))))
22.0ms	(/ x (fma 4.0 (pow p 2) (pow x 2)))
3.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
3.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series916.0ms

Counts

4 → 12

Calls

4 calls:

646.0ms	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3)) (fma (/ x (fma 4.0 (pow p 2) (pow x 2))) x (* (- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))) 1.0))))
82.0ms	(/ x (fma 4.0 (pow p 2) (pow x 2)))
97.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
92.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify3.2s

Counts

115 → 115

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	177	4308
1	331	4146
2	670	3947
3	1554	3650
4	4593	3644
done	5000	3643

prune833.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))
0.9b	(+ 1.0 (log (exp (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
2.5b	(log (exp (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
14.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

7.0ms	(/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))
46.0ms	(+ 1.0 (log (exp (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
21.0ms	(log (exp (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
3.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))
83.0ms	(+ 1.0 (log (exp (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
83.0ms	(log (exp (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
70.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify3.0s

Counts

125 → 125

Iterations

Useful iterations: 4 (713.0ms)

Iter	Nodes	Cost
0	164	2027
1	264	1711
2	498	1630
3	909	1629
4	2121	1628
done	5000	1628

prune588.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.3b

regimes105.0ms

Accuracy

0% (3.9b remaining)

Error of 13.6b against oracle of 9.8b and baseline of 13.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	21	18
done	21	18

end0.0ms

sample2.2s

Algorithm

intervals

Results

730.0ms	850×	body	2560	valid
465.0ms	5977×	body	80	valid
411.0ms	638×	body	1280	valid
149.0ms	8000×	pre	80	true
102.0ms	284×	body	640	valid
68.0ms	165×	body	320	valid
10.0ms	86×	body	160	valid