Details

Time bar (total: 31.6s)

sample335.0ms

Algorithm
intervals
Results
194.0ms118×body1280valid
69.0ms72×body640valid
16.0ms256×pre80true
11.0ms23×body320valid
5.0ms31×body80valid
4.0ms12×body160valid

simplify120.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
099
1159
2229
3339
4389
5459
6519
7619
8749
9869
10959
done959

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b
(+ x (- (tan (+ y z)) (tan a)))
0.2b
(- (tan (+ y z)) (tan a))
3.7b
(tan (+ y z))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
18×prod-diff
17×add-cube-cbrt
11×associate-+r+
10×add-log-exp
4×tan-quot
3×pow1 add-exp-log expm1-log1p-u fma-def fma-neg add-cbrt-cube log1p-expm1-u
2×sub-neg tan-sum diff-log sum-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 72
Calls
3 calls:
25.0ms
(+ x (- (tan (+ y z)) (tan a)))
24.0ms
(- (tan (+ y z)) (tan a))
7.0ms
(tan (+ y z))

series419.0ms

Counts
3 → 9
Calls
3 calls:
162.0ms
(+ x (- (tan (+ y z)) (tan a)))
181.0ms
(- (tan (+ y z)) (tan a))
76.0ms
(tan (+ y z))

simplify4.0s

Counts
81 → 81
Iterations

Useful iterations: done (4.0s)

IterNodesCost
01281195
12741008
2644882
32382793
done5000773

prune330.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b
(* (tan y) (tan z))

rewrite491.0ms

Algorithm
rewrite-expression-head
Rules
165×*-un-lft-identity
115×add-sqr-sqrt
108×add-cube-cbrt prod-diff
97×times-frac
56×associate-+r+
27×distribute-lft-out
18×fma-neg
16×associate-/r/
11×add-log-exp
9×flip3-- flip--
8×add-exp-log add-cbrt-cube div-inv
7×tan-quot
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-def associate-*r* associate-*l* associate-/r* associate-/l/
2×sub-neg flip3-+ diff-log sum-log flip-+ distribute-lft-out-- difference-of-squares
1×cbrt-undiv +-commutative frac-times associate-+r- frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ frac-add prod-exp clear-num *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 227
Calls
4 calls:
32.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
186.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
239.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
21.0ms
(* (tan y) (tan z))

series1.7s

Counts
4 → 12
Calls
4 calls:
338.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
577.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
627.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
131.0ms
(* (tan y) (tan z))

simplify1.5s

Counts
239 → 239
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03037323
16886202
217785656
done50005023

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (tan a))
0.7b
(cbrt (tan a))
0.7b
(cbrt (tan a))
60.6b
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×tan-quot cbrt-div pow1/3
1×fma-udef
Counts
4 → 52
Calls
4 calls:
4.0ms
(cbrt (tan a))
4.0ms
(cbrt (tan a))
4.0ms
(cbrt (tan a))
1.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series823.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(cbrt (tan a))
166.0ms
(cbrt (tan a))
226.0ms
(cbrt (tan a))
263.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify17.0s

Counts
64 → 64
Iterations

Useful iterations: 4 (939.0ms)

IterNodesCost
055644
1107463
2218367
3572357
41829307
done5000307

prune365.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
0.2b
(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
0.2b
(* (tan z) (tan y))
0.2b
(* (tan y) (tan z))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×tan-quot pow1
6×associate-*r* associate-*l*
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×times-frac prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv frac-times associate-*r/ div-exp pow-prod-down associate-/r/ *-commutative unswap-sqr
1×flip3-- frac-2neg clear-num associate-/r* flip-- fma-udef div-inv
Counts
4 → 81
Calls
4 calls:
0.0ms
(fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
14.0ms
(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
23.0ms
(* (tan z) (tan y))
16.0ms
(* (tan y) (tan z))

series990.0ms

Counts
4 → 12
Calls
4 calls:
301.0ms
(fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
491.0ms
(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
98.0ms
(* (tan z) (tan y))
99.0ms
(* (tan y) (tan z))

simplify1.8s

Counts
93 → 93
Iterations

Useful iterations: 3 (938.0ms)

IterNodesCost
01591853
13531769
210931543
340401513
done50001513

prune392.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes7.0ms