Details

sample133.0ms

Algorithm

intervals

Results

31.0ms	182×	body	80	valid
29.0ms	27×	body	2560	valid
27.0ms	30×	body	1280	valid
15.0ms	256×	pre	80	true
4.0ms	8×	body	320	valid
2.0ms	3×	body	640	valid
2.0ms	5×	body	160	valid
1.0ms	1×	body	5120	valid

simplify52.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	48
4	48
3	46
2	40
1	28
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma p (* 4 p) (* x x))
0.0b	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
1.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
15.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

0.0ms	(fma p (* 4 p) (* x x))
1.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series509.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma p (* 4 p) (* x x))
271.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
118.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
77.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify786.0ms

Counts

66 → 66

Iterations

Iter	Nodes
4	2276
3	582
2	178
1	96
0	70

prune634.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
1.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.7b	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
15.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `exp-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-prod` `fma-udef`
2×	`exp-sum`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

2.0ms	(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
2.0ms	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
92.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
102.0ms	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
71.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
5	2804
4	671
3	257
2	147
1	109
0	79

prune901.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5))
0.3b	(* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x)
5.3b	(+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5)
15.0b	(sqrt (fma (* p 4) p (* x x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`associate-l`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
16×	`sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `prod-exp` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sum-log` `fma-def` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

14.0ms	(sqrt (+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5))
12.0ms	(* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x)
24.0ms	(+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5)
3.0ms	(sqrt (fma (* p 4) p (* x x)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(sqrt (+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5))
85.0ms	(* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x)
107.0ms	(+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5)
59.0ms	(sqrt (fma (* p 4) p (* x x)))

simplify1.2s

Counts

106 → 106

Iterations

Iter	Nodes
3	2456
2	777
1	283
0	135

prune997.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.7b	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
15.0b	(sqrt (fma p (* 4 p) (* x x)))
15.0b	(sqrt (fma p (* 4 p) (* x x)))
15.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
8×	`pow1`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `exp-prod` `sqrt-pow1` `pow1/2`
1×	`rem-log-exp` `exp-sum` `fma-udef`

Counts

4 → 67

Calls

4 calls:

2.0ms	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
54.0ms	(sqrt (fma p (* 4 p) (* x x)))
61.0ms	(sqrt (fma p (* 4 p) (* x x)))
60.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify7.8s

Counts

79 → 79

Iterations

Iter	Nodes
6	8251
5	1552
4	435
3	199
2	124
1	90
0	66

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 15.0b

regimes136.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	18
1	18
0	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.0s	775×	body	2560	valid
704.0ms	5969×	body	80	valid
350.0ms	634×	body	1280	valid
283.0ms	8000×	pre	80	true
143.0ms	291×	body	640	valid
72.0ms	67×	body	5120	valid
55.0ms	180×	body	320	valid
18.0ms	84×	body	160	valid