Details

sample268.0ms

Algorithm

intervals

Results

125.0ms	101×	body	1280	valid
50.0ms	72×	body	640	valid
49.0ms	250×	body	80	valid
20.0ms	36×	body	320	valid
5.0ms	13×	body	160	valid

simplify126.0ms

Calls

1 calls:

Slowest

126.0ms

(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.2b	(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
92×	`times-frac`
76×	`*-un-lft-identity` `add-cube-cbrt`
58×	`sqrt-prod`
50×	`associate-l`
38×	`unswap-sqr`
36×	`associate-r`
32×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r` `associate-l/`
14×	`pow1`
12×	`swap-sqr` `prod-exp` `cbrt-unprod` `associate-/l*`
10×	`*-commutative`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Calls

4 calls:

Slowest

62.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
60.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms	(/ (cos th) (sqrt 2))
17.0ms	(/ (cos th) (sqrt 2))

series445.0ms

Calls

4 calls:

Slowest

151.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
137.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
84.0ms	(/ (cos th) (sqrt 2))
74.0ms	(/ (cos th) (sqrt 2))

simplify11.3s

Calls

274 calls:

Slowest

776.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
633.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
610.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
600.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
373.0ms	(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune3.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos th) (sqrt 2))
0.4b	(/ (* a2 (cos th)) (sqrt 2))
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.2b	(* a2 (/ (* a2 (cos th)) (sqrt 2)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

222×	`add-sqr-sqrt`
194×	`times-frac`
138×	`*-un-lft-identity`
136×	`associate-r` `add-cube-cbrt`
109×	`sqrt-prod`
71×	`associate-l`
40×	`unswap-sqr`
32×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
24×	`associate-/r*`
21×	`associate-*r/`
20×	`*-commutative`
12×	`associate-*l/`
11×	`pow1` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`swap-sqr`
5×	`clear-num`
4×	`expm1-log1p-u` `frac-2neg` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`un-div-inv`

Calls

4 calls:

Slowest

49.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
46.0ms	(* a2 (/ (* a2 (cos th)) (sqrt 2)))
30.0ms	(/ (* a2 (cos th)) (sqrt 2))
17.0ms	(/ (cos th) (sqrt 2))

series489.0ms

Calls

4 calls:

Slowest

145.0ms	(/ (* a2 (cos th)) (sqrt 2))
144.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
114.0ms	(* a2 (/ (* a2 (cos th)) (sqrt 2)))
85.0ms	(/ (cos th) (sqrt 2))

simplify14.7s

Calls

425 calls:

Slowest

613.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
586.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
434.0ms	(/ (* (cbrt a2) (cos th)) (sqrt (cbrt 2)))
392.0ms	(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
345.0ms	(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))

prune4.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* a2 (cos th)) (sqrt 2))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.2b	(* a2 (/ (* a2 (cos th)) (sqrt 2)))
0.1b	(* a2 (cos th))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

339×	`add-sqr-sqrt`
316×	`times-frac`
247×	`associate-r`
211×	`*-un-lft-identity`
209×	`add-cube-cbrt`
167×	`sqrt-prod`
91×	`associate-l`
71×	`unswap-sqr`
54×	`associate-/l*`
37×	`*-commutative`
29×	`add-cbrt-cube` `add-exp-log`
28×	`swap-sqr`
21×	`associate-*r/`
18×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod`
8×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `clear-num` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `un-div-inv` `div-inv`
2×	`pow-prod-down`

Calls

4 calls:

Slowest

59.0ms	(* a2 (/ (* a2 (cos th)) (sqrt 2)))
58.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
18.0ms	(/ (* a2 (cos th)) (sqrt 2))
7.0ms	(* a2 (cos th))

series552.0ms

Calls

4 calls:

Slowest

179.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
169.0ms	(/ (* a2 (cos th)) (sqrt 2))
149.0ms	(* a2 (/ (* a2 (cos th)) (sqrt 2)))
54.0ms	(* a2 (cos th))

simplify27.2s

Calls

678 calls:

Slowest

435.0ms	(/ (* (cos th) (* (* (cbrt a1) (cbrt a1)) (* (cbrt a1) (cbrt a1)))) 1)
305.0ms	(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
304.0ms	(/ (* (cos th) (* a1 (* (cbrt a1) (cbrt a1)))) 1)
299.0ms	(* (* (* a2 a2) a2) (* (* (cos th) (cos th)) (cos th)))
292.0ms	(/ (* (cos th) (* a1 (sqrt a1))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

prune6.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

18.8b	(sqrt (* a1 a1))
18.8b	(sqrt (* a1 a1))
0.4b	(/ (* a2 (cos th)) (sqrt 2))
0.2b	(* (/ (* (cos th) (sqrt (* a1 a1))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (* a1 a1)) (cbrt (sqrt 2))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

17434×	`add-sqr-sqrt`
9885×	`sqrt-prod`
7356×	`unswap-sqr`
7202×	`cbrt-prod`
6031×	`times-frac`
2682×	`associate-l`
2609×	`swap-sqr`
2578×	`associate-r`
2427×	`associate-/l*`
2340×	`frac-times`
2294×	`*-un-lft-identity`
2293×	`add-cube-cbrt`
2050×	`associate-/r*`
1201×	`*-commutative`
131×	`add-cbrt-cube`
112×	`clear-num`
111×	`frac-2neg`
78×	`associate-*l/`
73×	`cbrt-unprod`
54×	`cbrt-undiv`
50×	`add-exp-log`
30×	`associate-*r/`
22×	`pow1`
19×	`prod-exp`
15×	`div-exp`
12×	`sqrt-pow1`
10×	`rem-sqrt-square`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`pow2` `pow-plus` `pow1/2` `pow-sqr` `un-div-inv` `pow-prod-up`

Calls

4 calls:

Slowest

467.0ms	(* (/ (* (cos th) (sqrt (* a1 a1))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (* a1 a1)) (cbrt (sqrt 2))))
26.0ms	(/ (* a2 (cos th)) (sqrt 2))
20.0ms	(sqrt (* a1 a1))
12.0ms	(sqrt (* a1 a1))

series371.0ms

Calls

4 calls:

Slowest

184.0ms	(/ (* a2 (cos th)) (sqrt 2))
156.0ms	(* (/ (* (cos th) (sqrt (* a1 a1))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (* a1 a1)) (cbrt (sqrt 2))))
16.0ms	(sqrt (* a1 a1))
15.0ms	(sqrt (* a1 a1))