Details

sample73.0ms

Algorithm

intervals

Results

16.0ms	206×	body	80	valid
10.0ms	4×	body	160	valid
6.0ms	17×	body	1280	valid
6.0ms	256×	pre	80	true
4.0ms	9×	body	2560	valid
4.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid

simplify57.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
0.0b	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
1.5b	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
15.9b	(sqrt (fma p (* 4.0 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:

28.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
10.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
24.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
3.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

392.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
73.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
99.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
92.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify1.6s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	2082
2	588
1	230
0	128

prune669.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize22.0ms

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)))))
2.7b	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
15.9b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite66.0ms

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))
40.0ms	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
9.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
1.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) 0.5))
73.0ms	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
104.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
91.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify989.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1089
1	347
0	150

prune502.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
6.6b	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (sqrt (fma (* p 4.0) p (* x x))))))
15.9b	(sqrt (fma (* p 4.0) p (* x x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
5.0ms	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (sqrt (fma (* p 4.0) p (* x x))))))
1.0ms	(sqrt (fma (* p 4.0) p (* x x)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt x)
190.0ms	(cbrt x)
104.0ms	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (sqrt (fma (* p 4.0) p (* x x))))))
74.0ms	(sqrt (fma (* p 4.0) p (* x x)))

simplify1.7s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	3742
2	586
1	171
0	80

prune389.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize65.0ms

Local error

Found 4 expressions with local error:

3.2b	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (* (* (cbrt (sqrt (fma (* p 4.0) p (* x x)))) (cbrt (sqrt (fma (* p 4.0) p (* x x))))) (cbrt (sqrt (fma (* p 4.0) p (* x x))))))))
15.9b	(sqrt (fma (* p 4.0) p (* x x)))
15.9b	(sqrt (fma (* p 4.0) p (* x x)))
15.9b	(sqrt (fma (* p 4.0) p (* x x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`*-un-lft-identity` `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-+`

Counts

4 → 61

Calls

4 calls:

5.0ms	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (* (* (cbrt (sqrt (fma (* p 4.0) p (* x x)))) (cbrt (sqrt (fma (* p 4.0) p (* x x))))) (cbrt (sqrt (fma (* p 4.0) p (* x x))))))))
1.0ms	(sqrt (fma (* p 4.0) p (* x x)))
1.0ms	(sqrt (fma (* p 4.0) p (* x x)))
1.0ms	(sqrt (fma (* p 4.0) p (* x x)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ 1.0 (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (* (* (cbrt (sqrt (fma (* p 4.0) p (* x x)))) (cbrt (sqrt (fma (* p 4.0) p (* x x))))) (cbrt (sqrt (fma (* p 4.0) p (* x x))))))))
72.0ms	(sqrt (fma (* p 4.0) p (* x x)))
72.0ms	(sqrt (fma (* p 4.0) p (* x x)))
72.0ms	(sqrt (fma (* p 4.0) p (* x x)))

simplify1.7s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	2804
2	476
1	137
0	60

prune440.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.7b

regimes117.0ms

Accuracy

0% (0.5b remaining)

Error of 13.5b against oracle of 13.1b and baseline of 13.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

565.0ms	764×	body	2560	valid
365.0ms	6035×	body	80	valid
235.0ms	596×	body	1280	valid
152.0ms	8000×	pre	80	true
59.0ms	310×	body	640	valid
51.0ms	151×	body	320	valid
23.0ms	63×	body	5120	valid
7.0ms	81×	body	160	valid