Details

Time bar (total: 6.1m)

sample502.0ms

Algorithm
intervals
Results
252.0ms126×body1280valid
150.0ms65×body640valid
32.0ms256×pre80true
14.0ms16×body320valid
12.0ms41×body80valid
6.0ms8×body160valid

simplify55.0ms

Calls
1 calls:
Slowest
55.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize43.0ms

Local error

Found 3 expressions with local error:

3.6b
(tan (+ y z))
0.1b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite48.0ms

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
5×tan-quot
4×tan-sum
3×expm1-log1p-u pow1 +-commutative fma-def add-cbrt-cube fma-neg add-exp-log frac-sub insert-posit16 log1p-expm1-u
2×sum-log sub-neg diff-log distribute-lft-out distribute-lft-out--
1×associate-+r- flip3-+ flip3-- flip-+ flip-- difference-of-squares
Calls
3 calls:
Slowest
22.0ms
(+ x (- (tan (+ y z)) (tan a)))
19.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(tan (+ y z))

series399.0ms

Calls
3 calls:
Slowest
163.0ms
(+ x (- (tan (+ y z)) (tan a)))
160.0ms
(- (tan (+ y z)) (tan a))
76.0ms
(tan (+ y z))

simplify3.8s

Calls
59 calls:
Slowest
270.0ms
(- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))
251.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
202.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
201.0ms
(fma 1 (tan (+ y z)) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
199.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune988.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite966.0ms

Algorithm
rewrite-expression-head
Rules
857×*-un-lft-identity
590×associate-*l*
523×add-sqr-sqrt
382×distribute-lft-out--
342×times-frac
156×difference-of-squares
139×unswap-sqr
89×add-cube-cbrt
77×distribute-lft-out
69×associate-*r*
23×*-commutative
19×associate-*l/ associate-/l*
18×associate-/r*
15×add-cbrt-cube add-exp-log
14×tan-quot
10×pow1
8×associate-/l/
6×frac-sub
5×flip3-- flip--
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow-prod-down frac-add flip-+
2×frac-times cbrt-undiv div-exp associate-*r/ associate-/r/
1×clear-num frac-2neg div-sub div-inv
Calls
4 calls:
Slowest
864.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
38.0ms
(* (+ (tan z) (tan y)) (cos a))
25.0ms
(* (tan z) (tan y))
14.0ms
(* (tan z) (tan y))

series1.1s

Calls
4 calls:
Slowest
648.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
196.0ms
(* (+ (tan z) (tan y)) (cos a))
136.0ms
(* (tan z) (tan y))
117.0ms
(* (tan z) (tan y))

simplify2.8m

Calls
776 calls:
Slowest
889.0ms
(/ (- (* (sqrt (+ (tan z) (tan y))) (sqrt (cos a))) (* (sqrt (- 1 (* (tan z) (tan y)))) (sqrt (sin a)))) (* (sqrt (- 1 (* (tan z) (tan y)))) (sqrt (cos a))))
883.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
856.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
753.0ms
(/ (sqrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))) (sqrt (- 1 (* (tan z) (tan y)))))
736.0ms
(/ (- (* (sqrt (+ (tan z) (tan y))) (sqrt (cos a))) (* (sqrt (- 1 (* (tan z) (tan y)))) (sqrt (sin a)))) (cbrt (* (- 1 (* (tan z) (tan y))) (cos a))))

prune9.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
673×*-un-lft-identity
583×add-sqr-sqrt
394×associate-*l*
281×times-frac
260×distribute-lft-out--
250×associate-*r/
243×frac-add
191×add-cube-cbrt
183×associate-/r*
180×associate-/l*
169×associate-*l/
168×associate-/l/
166×frac-sub
140×difference-of-squares
126×unswap-sqr
85×flip3-- flip--
56×clear-num frac-2neg associate-*r*
18×*-commutative
15×add-cbrt-cube add-exp-log
8×pow1
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+
2×distribute-rgt-in +-commutative distribute-lft-in pow-prod-down associate-/r/ div-inv distribute-lft-out
1×frac-times quot-tan div-sub
Calls
4 calls:
Slowest
1.8s
(/ (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
81.0ms
(* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))))
16.0ms
(/ (sin y) (cos y))
14.0ms
(* (tan z) (tan y))

series1.2s

Calls
4 calls:
Slowest
791.0ms
(/ (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
241.0ms
(* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))))
119.0ms
(* (tan z) (tan y))
35.0ms
(/ (sin y) (cos y))

simplify2.8m

Calls
889 calls:
Slowest
953.0ms
(/ (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
816.0ms
(/ (* (* (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a))) (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a)))) (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a)))) (* (* (* (- 1 (* (tan z) (tan y))) (cos a)) (* (- 1 (* (tan z) (tan y))) (cos a))) (* (- 1 (* (tan z) (tan y))) (cos a))))
784.0ms
(- (* (* (cos a) (+ (* 1 (- (cos y))) (* (/ (cos z) (sin z)) (- (sin y))))) (+ 1 (* (tan z) (tan y)))) (* (* (/ (cos z) (sin z)) (- (cos y))) (* (- (* 1 1) (* (* (tan z) (tan y)) (* (tan z) (tan y)))) (sin a))))
745.0ms
(/ (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
707.0ms
(/ (* (* (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a))) (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a)))) (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a)))) (* (* (* (- 1 (* (tan z) (tan y))) (- 1 (* (tan z) (tan y)))) (- 1 (* (tan z) (tan y)))) (* (* (cos a) (cos a)) (cos a))))

prune11.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos a))
0.3b
(cbrt (cos a))
0.3b
(cbrt (cos a))
0.2b
(* (/ 1 (* (- 1 (* (tan z) (tan y))) (* (cbrt (cos a)) (cbrt (cos a))))) (/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (cbrt (cos a))))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
3303×add-sqr-sqrt
3198×*-un-lft-identity
2192×associate-/r*
2076×associate-*l*
2016×frac-times
1438×associate-*r*
1232×distribute-lft-out--
1207×associate-/l*
1174×cbrt-prod
1153×unswap-sqr
751×add-cube-cbrt
742×associate-*l/
456×associate-/l/
412×difference-of-squares
366×times-frac
342×frac-sub
332×swap-sqr
256×distribute-lft-out
229×flip3-- flip--
228×tan-quot
127×*-commutative
114×flip3-+ frac-add flip-+
95×clear-num
94×frac-2neg
86×add-cbrt-cube
78×add-exp-log
48×cbrt-unprod
38×prod-exp
36×associate-*r/
32×cbrt-undiv
22×div-exp
14×un-div-inv
6×pow1 rec-exp 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×associate-/r/ div-inv
1×pow-prod-down
Calls
4 calls:
Slowest
1.6s
(* (/ 1 (* (- 1 (* (tan z) (tan y))) (* (cbrt (cos a)) (cbrt (cos a))))) (/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (cbrt (cos a))))
1.0ms
(cbrt (cos a))
1.0ms
(cbrt (cos a))
1.0ms
(cbrt (cos a))

series868.0ms

Calls
4 calls:
Slowest
534.0ms
(* (/ 1 (* (- 1 (* (tan z) (tan y))) (* (cbrt (cos a)) (cbrt (cos a))))) (/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (cbrt (cos a))))
125.0ms
(cbrt (cos a))
104.0ms
(cbrt (cos a))
104.0ms
(cbrt (cos a))