Details

sample78.0ms

Algorithm

intervals

Results

17.0ms	194×	body	80	valid
16.0ms	25×	body	2560	valid
9.0ms	20×	body	1280	valid
7.0ms	256×	pre	80	true
4.0ms	11×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite147.0ms

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
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` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

23.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
22.0ms	(+ (* (* 4.0 p) p) (* x x))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
51.0ms	(+ (* (* 4.0 p) p) (* x x))
105.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
85.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5002
2	1518
1	320
0	135

prune656.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.1b

localize39.0ms

Local error

Found 4 expressions with local error:

5.4b	(+ 1.0 (* (* (/ (cbrt x) (* (cbrt (sqrt (fma 4.0 (* p p) (* x x)))) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) (cbrt x)) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))))
14.2b	(sqrt (fma 4.0 (* p p) (* x x)))
14.2b	(sqrt (fma 4.0 (* p p) (* x x)))
14.2b	(sqrt (fma 4.0 (* p p) (* x x)))

rewrite19.0ms

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:

10.0ms	(+ 1.0 (* (* (/ (cbrt x) (* (cbrt (sqrt (fma 4.0 (* p p) (* x x)))) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) (cbrt x)) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))))
2.0ms	(sqrt (fma 4.0 (* p p) (* x x)))
2.0ms	(sqrt (fma 4.0 (* p p) (* x x)))
2.0ms	(sqrt (fma 4.0 (* p p) (* x x)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ 1.0 (* (* (/ (cbrt x) (* (cbrt (sqrt (fma 4.0 (* p p) (* x x)))) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) (cbrt x)) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))))
86.0ms	(sqrt (fma 4.0 (* p p) (* x x)))
87.0ms	(sqrt (fma 4.0 (* p p) (* x x)))
78.0ms	(sqrt (fma 4.0 (* p p) (* x x)))

simplify1.9s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	3211
2	506
1	137
0	60

prune565.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.1b

localize32.0ms

Local error

Found 4 expressions with local error:

5.4b	(+ (* (* (/ (cbrt x) (* (cbrt (sqrt (fma 4.0 (* p p) (* x x)))) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) (cbrt x)) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) 1.0)
14.2b	(sqrt (fma 4.0 (* p p) (* x x)))
14.2b	(sqrt (fma 4.0 (* p p) (* x x)))
14.2b	(sqrt (fma 4.0 (* p p) (* x x)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

101.0ms	(+ (* (* (/ (cbrt x) (* (cbrt (sqrt (fma 4.0 (* p p) (* x x)))) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) (cbrt x)) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) 1.0)
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)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (* (* (/ (cbrt x) (* (cbrt (sqrt (fma 4.0 (* p p) (* x x)))) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) (cbrt x)) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (* p p) (* x x)))))) 1.0)
64.0ms	(sqrt (fma 4.0 (* p p) (* x x)))
64.0ms	(sqrt (fma 4.0 (* p p) (* x x)))
64.0ms	(sqrt (fma 4.0 (* p p) (* x x)))

simplify1.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
3	2849
2	482
1	139
0	60

prune465.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
0.5b	(expm1 (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))))
0.7b	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
14.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

0.0ms	(log1p (expm1 (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
0.0ms	(expm1 (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))))
16.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(log1p (expm1 (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))))
174.0ms	(expm1 (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))))
85.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
66.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.7s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
4	3438
3	1040
2	359
1	157
0	78

prune268.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

regimes115.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample1.6s

Algorithm

intervals

Results

421.0ms	8000×	pre	80	true
352.0ms	6045×	body	80	valid
258.0ms	728×	body	2560	valid
141.0ms	624×	body	1280	valid
62.0ms	331×	body	640	valid
45.0ms	62×	body	5120	valid
43.0ms	138×	body	320	valid
6.0ms	72×	body	160	valid