Details

sample84.0ms

Algorithm

intervals

Results

29.0ms	23×	body	2560	valid
13.0ms	188×	body	80	valid
7.0ms	20×	body	1280	valid
6.0ms	256×	pre	80	true
4.0ms	14×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	5120	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.0b	(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
1.2b	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
12.6b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

8.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
24.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
31.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
423.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
120.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
104.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.3s

Counts

100 → 100

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	128	1655
1	230	1487
2	590	1407
3	2066	1407
done	5001	1405

prune759.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
0.9b	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
1.2b	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
12.6b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

27.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
5.0ms	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
24.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series982.0ms

Counts

4 → 12

Calls

4 calls:

424.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))
362.0ms	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
92.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
103.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.8s

Counts

77 → 77

Iterations

Useful iterations: 4 (664.0ms)

Iter	Nodes	Cost
0	104	1282
1	182	1153
2	394	1075
3	956	1053
4	2781	1051
done	5000	1051

prune717.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize36.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
12.6b	(sqrt (fma (* 4.0 p) p (* x x)))
12.6b	(sqrt (fma (* 4.0 p) p (* x x)))
12.6b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

12.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
100.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
88.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
92.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.5s

Counts

74 → 74

Iterations

Useful iterations: 4 (552.0ms)

Iter	Nodes	Cost
0	56	882
1	120	793
2	282	746
3	702	735
4	1983	734
done	5001	734

prune779.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.3b

localize77.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
12.6b	(sqrt (fma (* 4.0 p) p (* x x)))
12.6b	(sqrt (fma (* 4.0 p) p (* x x)))
12.6b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1`
5×	`log-pow`
4×	`expm1-log1p-u` `log-prod` `exp-prod` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`rem-log-exp` `exp-sum` `distribute-lft-out`

Counts

4 → 64

Calls

4 calls:

72.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
99.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
111.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
113.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify911.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	64	961
1	85	845
2	148	784
3	301	784
4	1171	784
done	5000	784

prune764.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 14.3b

regimes420.0ms

Accuracy

0% (0.5b remaining)

Error of 13.9b against oracle of 13.3b and baseline of 13.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	51
1	25	51
done	25	51

end0.0ms

sample2.5s

Algorithm

intervals

Results

884.0ms	796×	body	2560	valid
488.0ms	5963×	body	80	valid
366.0ms	615×	body	1280	valid
211.0ms	8000×	pre	80	true
120.0ms	323×	body	640	valid
81.0ms	163×	body	320	valid
33.0ms	54×	body	5120	valid
13.0ms	86×	body	160	valid