Details

sample70.0ms

Algorithm

intervals

Results

15.0ms	203×	body	80	valid
12.0ms	6×	body	160	valid
8.0ms	18×	body	1280	valid
6.0ms	256×	pre	80	true
4.0ms	13×	body	640	valid
3.0ms	16×	body	320	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2747
3	478
2	106
1	31
0	15

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

0.1b

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

12.7b

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
156×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
24×	`associate-/l*`
20×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`flip3-+` `flip3--` `flip-+` `fma-udef` `flip--`

Counts

3 → 169

Calls

3 calls:

27.0ms

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

53.0ms

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

1.0ms

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

series645.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

238.0ms

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

282.0ms

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

simplify1.5s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	2673
1	620
0	250

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
0.0b	(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
0.1b	(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
1.6b	(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
66×	`times-frac`
42×	`add-cube-cbrt`
22×	`associate-l`
20×	`add-cbrt-cube` `add-exp-log`
19×	`associate-r`
18×	`distribute-lft-out`
9×	`associate-/l*`
7×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `unswap-sqr` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `+-commutative` `sum-log` `fma-def` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 163

Calls

4 calls:

39.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
15.0ms	(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
71.0ms	(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
25.0ms	(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

series924.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
125.0ms	(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
371.0ms	(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
289.0ms	(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

simplify2.0s

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
2	4161
1	716
0	242

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) 3)
1.6b	(+ (pow 1.0 3) (pow (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) 3))
1.8b	(- 1.0 (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))))
2.0b	(/ (* (/ (* (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (* (- beta alpha) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) (fma i 2.0 (+ alpha beta)))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-cbrt-cube` `add-exp-log`
53×	`*-un-lft-identity`
33×	`add-sqr-sqrt` `cbrt-undiv` `div-exp`
31×	`add-cube-cbrt`
30×	`prod-diff`
28×	`prod-exp` `cbrt-unprod`
23×	`times-frac`
17×	`unpow-prod-down` `cube-prod`
12×	`fma-def`
11×	`associate-/l/`
10×	`associate-/r/` `distribute-lft-out`
9×	`frac-times`
8×	`add-log-exp`
7×	`associate-*r/`
6×	`flip3-+` `flip-+` `div-inv`
5×	`pow1` `flip3--` `associate-*l/` `flip--`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `rem-cube-cbrt`
3×	`pow-unpow` `associate-/r*` `fma-neg`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`cube-div` `pow-to-exp` `+-commutative` `clear-num` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `sum-cubes` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 182

Calls

4 calls:

23.0ms	(pow (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) 3)
92.0ms	(+ (pow 1.0 3) (pow (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) 3))
36.0ms	(- 1.0 (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))))
105.0ms	(/ (* (/ (* (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (* (- beta alpha) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) (fma i 2.0 (+ alpha beta)))

series18.1s

Counts

4 → 12

Calls

4 calls:

5.0s	(pow (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) 3)
10.0s	(+ (pow 1.0 3) (pow (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) 3))
448.0ms	(- 1.0 (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))))
2.6s	(/ (* (/ (* (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (* (- beta alpha) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) (fma i 2.0 (+ alpha beta)))

simplify638.0ms

Counts

194 → 194

Iterations

Iter	Nodes
done	5001
1	1378
0	397

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.2b

localize152.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (pow (pow 1.0 3) 3) (pow (pow (* (/ (- beta alpha) (fma i 2.0 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))) 3) 3))
1.8b	(- (pow (* (/ (- beta alpha) (fma i 2.0 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))) 3) (pow 1.0 3))
1.8b	(- 1.0 (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))))
2.0b	(/ (* (/ (* (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (* (- beta alpha) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) (fma i 2.0 (+ alpha beta)))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

126×	`prod-diff`
87×	`*-un-lft-identity`
79×	`add-sqr-sqrt`
72×	`add-cbrt-cube` `add-exp-log`
67×	`add-cube-cbrt`
61×	`unpow-prod-down` `cube-prod`
30×	`fma-def` `sqr-pow`
29×	`cbrt-undiv` `div-exp`
26×	`prod-exp` `cbrt-unprod`
24×	`cube-mult` `unpow3`
15×	`times-frac`
11×	`fma-neg` `associate-/l/`
10×	`add-log-exp`
9×	`frac-times` `difference-of-squares`
8×	`distribute-lft-out`
7×	`associate-*r/`
6×	`flip3--` `associate-/r/` `flip--`
5×	`associate-*l/`
4×	`expm1-log1p-u` `pow1` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `distribute-lft-out--`
1×	`difference-cubes` `+-commutative` `clear-num` `sum-log` `frac-2neg` `sum-cubes` `associate-/l*`

Counts

4 → 282

Calls

4 calls:

82.0ms	(+ (pow (pow 1.0 3) 3) (pow (pow (* (/ (- beta alpha) (fma i 2.0 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))) 3) 3))
40.0ms	(- (pow (* (/ (- beta alpha) (fma i 2.0 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))) 3) (pow 1.0 3))
37.0ms	(- 1.0 (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))))
144.0ms	(/ (* (/ (* (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (* (- beta alpha) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) (fma i 2.0 (+ alpha beta)))

series9.5m

Calls

3 calls:

9.8s

(- (pow (* (/ (- beta alpha) (fma i 2.0 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))) 3) (pow 1.0 3))

461.0ms

(- 1.0 (/ (* (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))))

2.4s

(/ (* (/ (* (/ (+ alpha beta) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) (+ 2.0 (fma i 2.0 (+ alpha beta)))) (* (- beta alpha) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) (fma i 2.0 (+ alpha beta)))