Details

sample80.0ms

Algorithm

intervals

Results

21.0ms	256×	pre	80	true
15.0ms	195×	body	80	valid
10.0ms	22×	body	2560	valid
9.0ms	25×	body	1280	valid
2.0ms	8×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
0.0b	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
0.9b	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
13.8b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite47.0ms

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:

5.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
14.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
14.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
12.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series683.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
378.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
126.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
86.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	2063
2	590
1	230
0	128

prune633.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))) 0.5))
0.2b	(* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))
2.6b	(+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x))))))
13.8b	(sqrt (fma (* p 4.0) p (* x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-l`
2×	`flip3-+` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-*l/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `1-exp` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

12.0ms	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))) 0.5))
33.0ms	(* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))
5.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x))))))
1.0ms	(sqrt (fma (* p 4.0) p (* x x)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

423.0ms	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))) 0.5))
86.0ms	(* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))
131.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x))))))
109.0ms	(sqrt (fma (* p 4.0) p (* x x)))

simplify793.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	1089
1	347
0	150

prune636.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))) 0.5))
0.2b	(* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))
2.6b	(+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x))))))
13.8b	(sqrt (fma (* p 4.0) p (* x x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-l`
2×	`flip3-+` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-*l/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `1-exp` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

6.0ms	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))) 0.5))
26.0ms	(* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))
5.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x))))))
1.0ms	(sqrt (fma (* p 4.0) p (* x x)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

404.0ms	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))) 0.5))
92.0ms	(* x (/ 1 (sqrt (fma (* p 4.0) p (* x x)))))
141.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* p 4.0) p (* x x))))))
99.0ms	(sqrt (fma (* p 4.0) p (* x x)))

simplify859.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	1089
1	347
0	150

prune710.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)))
0.7b	(log (exp (sqrt (* 0.5 (+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)))))
0.9b	(+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)
13.8b	(sqrt (fma (* p 4.0) p (* x x)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

22×	`fma-def` `*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
14×	`sqrt-prod`
9×	`pow1`
6×	`add-log-exp`
5×	`log-pow`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`log-prod` `sqrt-pow1`
2×	`flip3-+` `pow1/2` `sqrt-div` `associate-*r/` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `rem-log-exp` `pow-prod-down` `div-inv` `distribute-lft-out`

Counts

4 → 84

Calls

4 calls:

34.0ms	(sqrt (* 0.5 (+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)))
5.0ms	(log (exp (sqrt (* 0.5 (+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)))))
44.0ms	(+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)
3.0ms	(sqrt (fma (* p 4.0) p (* x x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

439.0ms	(sqrt (* 0.5 (+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)))
441.0ms	(log (exp (sqrt (* 0.5 (+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)))))
122.0ms	(+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)
108.0ms	(sqrt (fma (* p 4.0) p (* x x)))

simplify1.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
4	3104
3	1075
2	425
1	194
0	104

prune767.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.8b

regimes329.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample2.2s

Algorithm

intervals

Results

748.0ms	741×	body	2560	valid
473.0ms	6015×	body	80	valid
267.0ms	639×	body	1280	valid
263.0ms	8000×	pre	80	true
74.0ms	301×	body	640	valid
30.0ms	59×	body	5120	valid
29.0ms	153×	body	320	valid
11.0ms	92×	body	160	valid