Details

sample39.0ms

Algorithm

intervals

Results

16.0ms

428×

body

valid

simplify77.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	15	15
1	27	14
2	60	12
3	107	12
4	126	12
5	128	12
done	128	12

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a b (fma x y (* z t)))
0.0b	(fma x y (* z t))
0.0b	(fma c i (fma a b (fma x y (* z t))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

3 → 30

Calls

3 calls:

0.0ms	(fma a b (fma x y (* z t)))
0.0ms	(fma x y (* z t))
0.0ms	(fma c i (fma a b (fma x y (* z t))))

series343.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(fma a b (fma x y (* z t)))
38.0ms	(fma x y (* z t))
237.0ms	(fma c i (fma a b (fma x y (* z t))))

simplify1.1s

Counts

39 → 39

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	47	430
1	63	420
2	131	366
3	508	366
4	2870	366
done	5000	366

prune157.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a b (fma x y (* z t)))
0.0b	(fma x y (* z t))
0.0b	(+ (* c i) (fma a b (fma x y (* z t))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+r+` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

3 → 35

Calls

3 calls:

0.0ms	(fma a b (fma x y (* z t)))
0.0ms	(fma x y (* z t))
3.0ms	(+ (* c i) (fma a b (fma x y (* z t))))

series333.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(fma a b (fma x y (* z t)))
39.0ms	(fma x y (* z t))
227.0ms	(+ (* c i) (fma a b (fma x y (* z t))))

simplify740.0ms

Counts

44 → 44

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	60	559
1	133	504
2	364	468
3	1519	468
done	5000	468

prune172.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x y (* z t))
0.0b	(fma c i (fma a b (cbrt (pow (fma x y (* z t)) 3))))
0.3b	(pow (fma x y (* z t)) 3)
35.0b	(cbrt (pow (fma x y (* z t)) 3))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

0.0ms	(fma x y (* z t))
0.0ms	(fma c i (fma a b (cbrt (pow (fma x y (* z t)) 3))))
1.0ms	(pow (fma x y (* z t)) 3)
2.0ms	(cbrt (pow (fma x y (* z t)) 3))

series453.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma x y (* z t))
237.0ms	(fma c i (fma a b (cbrt (pow (fma x y (* z t)) 3))))
131.0ms	(pow (fma x y (* z t)) 3)
41.0ms	(cbrt (pow (fma x y (* z t)) 3))

simplify2.0s

Counts

80 → 80

Iterations

Useful iterations: 3 (498.0ms)

Iter	Nodes	Cost
0	99	1087
1	205	878
2	624	787
3	3646	785
done	5001	785

prune304.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (fma a b (fma x y (* z t))) 3)
1.6b	(fma (* c i) (* c i) (* (fma a b (fma x y (* z t))) (- (fma a b (fma x y (* z t))) (* c i))))
5.0b	(+ (pow (* c i) 3) (pow (fma a b (fma x y (* z t))) 3))
42.8b	(/ (+ (pow (* c i) 3) (pow (fma a b (fma x y (* z t))) 3)) (fma (* c i) (* c i) (* (fma a b (fma x y (* z t))) (- (fma a b (fma x y (* z t))) (* c i)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
18×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
8×	`fma-def`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `sum-cubes` `distribute-lft-out` `associate-/l*`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r*`
2×	`cube-mult` `flip3-+` `unpow3` `flip-+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `sum-log` `fma-udef` `div-inv` `rem-cube-cbrt`

Counts

4 → 97

Calls

4 calls:

1.0ms	(pow (fma a b (fma x y (* z t))) 3)
0.0ms	(fma (* c i) (* c i) (* (fma a b (fma x y (* z t))) (- (fma a b (fma x y (* z t))) (* c i))))
11.0ms	(+ (pow (* c i) 3) (pow (fma a b (fma x y (* z t))) 3))
33.0ms	(/ (+ (pow (* c i) 3) (pow (fma a b (fma x y (* z t))) 3)) (fma (* c i) (* c i) (* (fma a b (fma x y (* z t))) (- (fma a b (fma x y (* z t))) (* c i)))))

series9.9m

Calls

1 calls:

2.0s	(/ (+ (pow (* c i) 3) (pow (fma a b (fma x y (* z t))) 3)) (fma (* c i) (* c i) (* (fma a b (fma x y (* z t))) (- (fma a b (fma x y (* z t))) (* c i)))))