Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	32×	body	2560	valid
6.0ms	182×	body	80	valid
5.0ms	28×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	10×	body	640	valid
0.0ms	4×	body	320	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	39	16
3	46	16
4	48	16
5	50	16
6	51	16
done	51	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.1b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
14.9b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

15.0ms	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
3.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
16.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
59.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
78.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
62.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.9s

Counts

119 → 119

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	128	1655
1	224	1507
2	482	1405
3	1287	1405
4	3925	1405
done	5001	1405

prune353.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (cbrt (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3)) 1.0)
0.1b	(pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3)
14.9b	(sqrt (fma (* 4.0 p) p (* x x)))
16.3b	(cbrt (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
100×	`cbrt-prod`
89×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
66×	`unpow-prod-down` `cube-prod`
57×	`sqrt-prod`
53×	`fma-def`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-mult` `pow-unpow` `unpow3` `sqr-pow`
2×	`cube-div` `pow-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `cbrt-div` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `div-exp` `sum-log` `rem-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

4 → 210

Calls

4 calls:

66.0ms	(+ (cbrt (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3)) 1.0)
6.0ms	(pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3)
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
6.0ms	(cbrt (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3))

series337.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (cbrt (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3)) 1.0)
112.0ms	(pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3)
62.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
66.0ms	(cbrt (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3))

simplify556.0ms

Counts

222 → 222

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	190	4003
1	469	3318
2	1549	2913
done	5001	2913

prune493.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

Local error

Found 4 expressions with local error:

9.8b	(+ (cbrt (pow (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 3)) 1.0)
14.9b	(sqrt (fma (* 4.0 p) p (* x x)))
14.9b	(sqrt (fma (* 4.0 p) p (* x x)))
16.3b	(cbrt (pow (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-prod`
23×	`fma-def`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
12×	`times-frac`
6×	`pow1` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
2×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`
1×	`+-commutative` `cube-div` `cbrt-div` `flip3-+` `pow1/3` `sum-log` `rem-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

34.0ms	(+ (cbrt (pow (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 3)) 1.0)
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
4.0ms	(cbrt (pow (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 3))

series272.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (cbrt (pow (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 3)) 1.0)
59.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
56.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
64.0ms	(cbrt (pow (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 3))

simplify1.0s

Counts

111 → 111

Iterations

Useful iterations: 3 (377.0ms)

Iter	Nodes	Cost
0	113	2303
1	245	1260
2	759	1162
3	3030	1146
done	5000	1146

prune361.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 15.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
2.8b	(+ (* (/ (cbrt (* x x)) (fabs (cbrt (fma (* 4.0 p) p (* x x))))) (/ (cbrt x) (sqrt (cbrt (fma (* 4.0 p) p (* x x)))))) 1.0)
15.7b	(cbrt (fma (* 4.0 p) p (* x x)))
15.7b	(cbrt (fma (* 4.0 p) p (* x x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

0.0ms	(cbrt x)
9.0ms	(+ (* (/ (cbrt (* x x)) (fabs (cbrt (fma (* 4.0 p) p (* x x))))) (/ (cbrt x) (sqrt (cbrt (fma (* 4.0 p) p (* x x)))))) 1.0)
0.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
1.0ms	(cbrt (fma (* 4.0 p) p (* x x)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt x)
157.0ms	(+ (* (/ (cbrt (* x x)) (fabs (cbrt (fma (* 4.0 p) p (* x x))))) (/ (cbrt x) (sqrt (cbrt (fma (* 4.0 p) p (* x x)))))) 1.0)
126.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
127.0ms	(cbrt (fma (* 4.0 p) p (* x x)))

simplify1.5s

Counts

65 → 65

Iterations

Useful iterations: 3 (459.0ms)

Iter	Nodes	Cost
0	131	1256
1	310	1214
2	951	1094
3	4379	1042
done	5000	1042

prune278.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.2b

regimes139.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.3b and baseline of 13.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	21	31
done	21	31

end0.0ms

sample811.0ms

Algorithm

intervals

Results

199.0ms	5975×	body	80	valid
179.0ms	823×	body	2560	valid
112.0ms	649×	body	1280	valid
105.0ms	8000×	pre	80	true
43.0ms	324×	body	640	valid
16.0ms	156×	body	320	valid
5.0ms	73×	body	160	valid