Details

sample214.0ms

Algorithm

intervals

Results

100.0ms

551×

body

valid

simplify149.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

148.0ms

(- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5)

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* w r) (* w r))
0.4b	(/ 2 (* r r))
0.1b	(fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)
0.0b	(- (+ 3 (/ 2 (* r r))) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
27×	`*-un-lft-identity`
21×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`prod-diff`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `fma-neg` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `pow-plus` `diff-log` `div-exp` `fma-udef` `distribute-lft-out--`
1×	`pow2` `clear-num` `associate-/r` `sum-log` `sub-neg` `frac-2neg` `flip3--` `swap-sqr` `associate-r` `associate-l` `associate--l+` `-commutative` `div-inv` `flip--` `associate--r+` `difference-of-squares`

Counts

4 → 109

Calls

4 calls:

Slowest

103.0ms	(- (+ 3 (/ 2 (* r r))) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))
38.0ms	(* (* w r) (* w r))
7.0ms	(/ 2 (* r r))
0.0ms	(fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)

series365.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

133.0ms	(- (+ 3 (/ 2 (* r r))) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))
122.0ms	(fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)
60.0ms	(/ 2 (* r r))
50.0ms	(* (* w r) (* w r))

simplify26.0s

Counts

139 → 121

Calls

139 calls:

Slowest

823.0ms	(* (* (* (* w w) w) (* (* r r) r)) (* (* (* w w) w) (* (* r r) r)))
769.0ms	(fma (- (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)) 1 (* (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5) 1))
701.0ms	(* (* (* (* w r) (* w r)) (* w r)) (* (* (* w r) (* w r)) (* w r)))
661.0ms	(* (* (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))
521.0ms	(fma (* (cbrt (+ 3 (/ 2 (* r r)))) (cbrt (+ 3 (/ 2 (* r r))))) (cbrt (+ 3 (/ 2 (* r r)))) (- (* (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5) 1)))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* w r) (* w r))
0.2b	(/ (/ 2 r) r)
0.1b	(fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)
0.0b	(- (+ 3 (/ (/ 2 r) r)) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
67×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
43×	`pow1`
21×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
13×	`associate-/l*`
12×	`prod-diff`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
5×	`div-inv` `distribute-lft-out`
4×	`expm1-log1p-u` `fma-neg` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`pow-plus` `diff-log` `fma-udef` `distribute-lft-out--`
1×	`pow2` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `swap-sqr` `associate-r` `associate-l` `associate--l+` `*-commutative` `flip--` `associate--r+` `difference-of-squares` `associate-/l/`

Counts

4 → 158

Calls

4 calls:

Slowest

69.0ms	(- (+ 3 (/ (/ 2 r) r)) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))
46.0ms	(* (* w r) (* w r))
12.0ms	(/ (/ 2 r) r)
0.0ms	(fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)

series342.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

150.0ms	(fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)
112.0ms	(- (+ 3 (/ (/ 2 r) r)) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))
49.0ms	(/ (/ 2 r) r)
32.0ms	(* (* w r) (* w r))

simplify29.4s

Counts

224 → 170

Calls

224 calls:

Slowest

909.0ms	(* (* (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)) (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))
858.0ms	(* (* (* (* w w) w) (* (* r r) r)) (* (* (* w w) w) (* (* r r) r)))
728.0ms	(* (* (* (* w r) (* w r)) (* w r)) (* (* (* w r) (* w r)) (* w r)))
655.0ms	(log1p (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5))
520.0ms	(fma (- (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5)) 1 (* (fma (/ (fma v -2 3) (/ (- 1 v) 0.125)) (* (* w r) (* w r)) 4.5) 1))

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (sqrt 2) 1) (/ r (/ (sqrt 2) r)))
0.4b	(* (* w r) (* w r))
0.4b	(/ (sqrt 2) r)
0.2b	(/ r (/ (sqrt 2) r))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

5774×	`times-frac`
2456×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
1317×	`sqrt-prod`
171×	`div-inv`
96×	`associate-/r*`
53×	`add-exp-log`
44×	`add-cbrt-cube`
43×	`pow1`
31×	`associate-/l*`
28×	`div-exp`
25×	`associate-/r/`
19×	`cbrt-undiv`
17×	`pow-prod-down`
8×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `1-exp`
2×	`pow-plus`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 1873

Calls

4 calls:

Slowest

23.0ms	(* (* w r) (* w r))
19.0ms	(/ (/ (sqrt 2) 1) (/ r (/ (sqrt 2) r)))
14.0ms	(/ (sqrt 2) r)
14.0ms	(/ r (/ (sqrt 2) r))

series308.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

110.0ms	(/ r (/ (sqrt 2) r))
101.0ms	(/ (/ (sqrt 2) 1) (/ r (/ (sqrt 2) r)))
54.0ms	(/ (sqrt 2) r)
41.0ms	(* (* w r) (* w r))

simplify8.5m

Counts

3533 → 1885

Calls

3533 calls:

Slowest

1.1s	(/ (sqrt (/ (sqrt 2) 1)) (/ (* (cbrt r) (cbrt r)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)))
1.0s	(/ (/ (sqrt (sqrt 2)) (sqrt 1)) (/ (* (cbrt r) (cbrt r)) (/ (sqrt 1) (* (cbrt r) (cbrt r)))))
918.0ms	(/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1) (/ (* (cbrt r) (cbrt r)) (/ (sqrt (* (cbrt 2) (cbrt 2))) 1)))
889.0ms	(/ (/ (sqrt 1) 1) (/ (sqrt r) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt r))))
809.0ms	(/ (/ (sqrt (* (cbrt 2) (cbrt 2))) 1) (/ (* (cbrt r) (cbrt r)) (/ (sqrt (sqrt 2)) (* (cbrt r) (cbrt r)))))

prune21.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* w r) (* w r))
0.4b	(/ (sqrt 2) r)
0.3b	(* (sqrt (sqrt 2)) (/ (sqrt 2) r))
0.2b	(* (/ (sqrt (sqrt 2)) r) (* (sqrt (sqrt 2)) (/ (sqrt 2) r)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
69×	`times-frac` `sqrt-prod`
54×	`*-un-lft-identity` `add-cube-cbrt`
50×	`pow1`
44×	`add-cbrt-cube` `add-exp-log`
41×	`associate-l`
24×	`associate-r`
21×	`pow-prod-down`
20×	`prod-exp` `cbrt-unprod`
9×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/l*`
4×	`expm1-log1p-u` `associate-*r/` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `div-inv`
2×	`pow-plus`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `swap-sqr` `associate-*l/`

Counts

4 → 196

Calls

4 calls:

Slowest

34.0ms	(* (/ (sqrt (sqrt 2)) r) (* (sqrt (sqrt 2)) (/ (sqrt 2) r)))
27.0ms	(* (* w r) (* w r))
13.0ms	(* (sqrt (sqrt 2)) (/ (sqrt 2) r))
4.0ms	(/ (sqrt 2) r)

series279.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(* (sqrt (sqrt 2)) (/ (sqrt 2) r))
70.0ms	(* (/ (sqrt (sqrt 2)) r) (* (sqrt (sqrt 2)) (/ (sqrt 2) r)))
47.0ms	(/ (sqrt 2) r)
29.0ms	(* (* w r) (* w r))