Details

Time bar (total: 12.7s)

sample32.0ms

Algorithm
intervals
Results
18.0ms337×body80valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 8 (1.4s)

IterNodesCost
01417
12517
24617
39517
415417
522417
634917
775517
8261115
done500015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (- 1.0 t) 2.0) (/ 2.0 z))
0.0b
(+ (/ (+ (* (- 1.0 t) 2.0) (/ 2.0 z)) t) (/ x y))
0.1b
(/ (+ (* (- 1.0 t) 2.0) (/ 2.0 z)) t)

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
11×add-sqr-sqrt add-cube-cbrt times-frac
7×add-log-exp
5×add-exp-log frac-add add-cbrt-cube
4×associate-*l/ associate-/l/
3×pow1 flip3-+ associate-/r* flip-+ associate-/l*
2×+-commutative flip3-- sum-log flip-- distribute-lft-out
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 58
Calls
3 calls:
20.0ms
(+ (* (- 1.0 t) 2.0) (/ 2.0 z))
138.0ms
(+ (/ (+ (* (- 1.0 t) 2.0) (/ 2.0 z)) t) (/ x y))
54.0ms
(/ (+ (* (- 1.0 t) 2.0) (/ 2.0 z)) t)

series136.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* (- 1.0 t) 2.0) (/ 2.0 z))
62.0ms
(+ (/ (+ (* (- 1.0 t) 2.0) (/ 2.0 z)) t) (/ x y))
47.0ms
(/ (+ (* (- 1.0 t) 2.0) (/ 2.0 z)) t)

simplify1.9s

Counts
67 → 67
Iterations

Useful iterations: 3 (859.0ms)

IterNodesCost
01331266
13541207
210281119
333071101
done50021101

prune215.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 2.0 (* t z)) (- (/ 2.0 t) 2.0))
0.0b
(+ (+ (/ 2.0 (* t z)) (- (/ 2.0 t) 2.0)) (/ x y))
0.5b
(/ 2.0 (* t z))

rewrite508.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
17×add-log-exp
8×add-exp-log frac-add add-cbrt-cube
7×sum-log distribute-lft-out
5×add-sqr-sqrt add-cube-cbrt
3×pow1 flip3-+ times-frac flip-+ associate-/l*
2×cbrt-undiv +-commutative associate-+r- associate-+r+ flip3-- diff-log div-exp flip-- distribute-lft-out--
1×associate-+l- sub-neg associate-+l+ frac-2neg prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 62
Calls
3 calls:
57.0ms
(+ (/ 2.0 (* t z)) (- (/ 2.0 t) 2.0))
436.0ms
(+ (+ (/ 2.0 (* t z)) (- (/ 2.0 t) 2.0)) (/ x y))
13.0ms
(/ 2.0 (* t z))

series130.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ (/ 2.0 (* t z)) (- (/ 2.0 t) 2.0))
61.0ms
(+ (+ (/ 2.0 (* t z)) (- (/ 2.0 t) 2.0)) (/ x y))
23.0ms
(/ 2.0 (* t z))

simplify920.0ms

Counts
71 → 71
Iterations

Useful iterations: done (917.0ms)

IterNodesCost
01391294
13941208
214341148
done50011106

prune256.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ (sqrt 2.0) (/ (* t z) (sqrt 2.0))) (- (/ 2.0 t) 2.0))
0.0b
(+ (+ (/ (sqrt 2.0) (/ (* t z) (sqrt 2.0))) (- (/ 2.0 t) 2.0)) (/ x y))
0.4b
(/ (* t z) (sqrt 2.0))
0.6b
(/ (sqrt 2.0) (/ (* t z) (sqrt 2.0)))

rewrite895.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
65×*-un-lft-identity
60×sqrt-prod
51×add-sqr-sqrt add-cube-cbrt
18×add-exp-log add-cbrt-cube add-log-exp
16×associate-/r*
9×div-inv
8×frac-add
7×cbrt-undiv div-exp sum-log distribute-lft-out associate-/l*
4×pow1
3×flip3-+ flip-+
2×+-commutative associate-+r- associate-+r+ flip3-- frac-2neg diff-log prod-exp clear-num flip-- cbrt-unprod distribute-lft-out--
1×associate-+l- sub-neg associate-+l+ associate-/r/
Counts
4 → 161
Calls
4 calls:
91.0ms
(+ (/ (sqrt 2.0) (/ (* t z) (sqrt 2.0))) (- (/ 2.0 t) 2.0))
766.0ms
(+ (+ (/ (sqrt 2.0) (/ (* t z) (sqrt 2.0))) (- (/ 2.0 t) 2.0)) (/ x y))
12.0ms
(/ (* t z) (sqrt 2.0))
20.0ms
(/ (sqrt 2.0) (/ (* t z) (sqrt 2.0)))

series494.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (/ (sqrt 2.0) (/ (* t z) (sqrt 2.0))) (- (/ 2.0 t) 2.0))
175.0ms
(+ (+ (/ (sqrt 2.0) (/ (* t z) (sqrt 2.0))) (- (/ 2.0 t) 2.0)) (/ x y))
110.0ms
(/ (* t z) (sqrt 2.0))
100.0ms
(/ (sqrt 2.0) (/ (* t z) (sqrt 2.0)))

simplify1.3s

Counts
173 → 173
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02583253
16562952
223132540
done50012459

prune527.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

2.8b
(+ (pow (/ 2.0 (* t z)) 3) (pow (- (/ 2.0 t) 2.0) 3))
4.8b
(* (+ (* (- (/ 2.0 t) 2.0) (- (- (/ 2.0 t) 2.0) (/ 2.0 (* t z)))) (* (/ 2.0 (* t z)) (/ 2.0 (* t z)))) x)
7.0b
(+ (* (+ (pow (/ 2.0 (* t z)) 3) (pow (- (/ 2.0 t) 2.0) 3)) y) (* (+ (* (- (/ 2.0 t) 2.0) (- (- (/ 2.0 t) 2.0) (/ 2.0 (* t z)))) (* (/ 2.0 (* t z)) (/ 2.0 (* t z)))) x))
26.5b
(/ (+ (* (+ (pow (/ 2.0 (* t z)) 3) (pow (- (/ 2.0 t) 2.0) 3)) y) (* (+ (* (- (/ 2.0 t) 2.0) (- (- (/ 2.0 t) 2.0) (/ 2.0 (* t z)))) (* (/ 2.0 (* t z)) (/ 2.0 (* t z)))) x)) (* y (+ (* (- (/ 2.0 t) 2.0) (- (- (/ 2.0 t) 2.0) (/ 2.0 (* t z)))) (* (/ 2.0 (* t z)) (/ 2.0 (* t z))))))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
950×frac-add
948×associate-*l/
419×flip3-- flip--
380×frac-times
356×cube-div
304×associate-*r/
180×frac-sub
178×associate-/l/
101×flip3-+ flip-+
44×associate-/r/
30×*-un-lft-identity
11×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×distribute-lft-out
8×add-cube-cbrt unpow-prod-down cube-prod add-log-exp
6×pow1
4×distribute-lft-out--
3×times-frac associate-*r* associate-*l* associate-/l*
2×cbrt-undiv +-commutative div-exp prod-exp sum-log cbrt-unprod
1×frac-2neg pow-prod-down clear-num associate-/r* sum-cubes *-commutative div-inv unswap-sqr
Counts
4 → 515
Calls
4 calls:
188.0ms
(+ (pow (/ 2.0 (* t z)) 3) (pow (- (/ 2.0 t) 2.0) 3))
474.0ms
(* (+ (* (- (/ 2.0 t) 2.0) (- (- (/ 2.0 t) 2.0) (/ 2.0 (* t z)))) (* (/ 2.0 (* t z)) (/ 2.0 (* t z)))) x)
326.0ms
(+ (* (+ (pow (/ 2.0 (* t z)) 3) (pow (- (/ 2.0 t) 2.0) 3)) y) (* (+ (* (- (/ 2.0 t) 2.0) (- (- (/ 2.0 t) 2.0) (/ 2.0 (* t z)))) (* (/ 2.0 (* t z)) (/ 2.0 (* t z)))) x))
1.1s
(/ (+ (* (+ (pow (/ 2.0 (* t z)) 3) (pow (- (/ 2.0 t) 2.0) 3)) y) (* (+ (* (- (/ 2.0 t) 2.0) (- (- (/ 2.0 t) 2.0) (/ 2.0 (* t z)))) (* (/ 2.0 (* t z)) (/ 2.0 (* t z)))) x)) (* y (+ (* (- (/ 2.0 t) 2.0) (- (- (/ 2.0 t) 2.0) (/ 2.0 (* t z)))) (* (/ 2.0 (* t z)) (/ 2.0 (* t z))))))

series2.0ms