Details

Time bar (total: 5.4m)

sample498.0ms

Algorithm
intervals
Results
311.0ms126×body1280valid
91.0ms65×body640valid
32.0ms256×pre80true
15.0ms16×body320valid
11.0ms41×body80valid
5.0ms8×body160valid

simplify65.0ms

Calls
1 calls:
Slowest
65.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize16.0ms

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)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt tan-quot
4×tan-sum
3×pow1 +-commutative add-cbrt-cube add-exp-log frac-sub add-cube-cbrt insert-posit16
2×associate-+r+ 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
24.0ms
(- (tan (+ y z)) (tan a))
10.0ms
(+ x (- (tan (+ y z)) (tan a)))
6.0ms
(tan (+ y z))

series333.0ms

Calls
3 calls:
Slowest
141.0ms
(+ x (- (tan (+ y z)) (tan a)))
140.0ms
(- (tan (+ y z)) (tan a))
51.0ms
(tan (+ y z))

simplify2.0s

Calls
28 calls:
Slowest
415.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
388.0ms
(- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))
154.0ms
(* (- 1 (* (tan z) (tan y))) (cos a))
146.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
112.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))

prune588.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite772.0ms

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×prod-exp cbrt-unprod insert-posit16 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
690.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
26.0ms
(* (tan y) (tan z))
23.0ms
(* (+ (tan y) (tan z)) (cos a))
18.0ms
(* (tan y) (tan z))

series1.2s

Calls
4 calls:
Slowest
713.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
219.0ms
(* (+ (tan y) (tan z)) (cos a))
141.0ms
(* (tan y) (tan z))
131.0ms
(* (tan y) (tan z))

simplify2.0m

Calls
776 calls:
Slowest
761.0ms
(/ (sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) 1)
733.0ms
(/ (- (* (sqrt (+ (tan y) (tan z))) (sqrt (cos a))) (* (sqrt (- 1 (* (tan y) (tan z)))) (sqrt (sin a)))) (* (sqrt (- 1 (* (tan y) (tan z)))) (sqrt (cos a))))
656.0ms
(/ (- (sqrt (* (+ (tan y) (tan z)) (cos a))) (* (sqrt (- 1 (* (tan y) (tan z)))) (sqrt (sin a)))) (* (- 1 (sqrt (* (tan y) (tan z)))) (cos a)))
639.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
529.0ms
(/ (sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (- 1 (* (tan y) (tan z))) 1))

prune5.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite647.0ms

Algorithm
rewrite-expression-head
Rules
2028×*-un-lft-identity
1372×add-sqr-sqrt
1215×times-frac
827×associate-*l*
820×distribute-lft-out--
456×difference-of-squares
306×add-cube-cbrt
305×unswap-sqr
196×associate-/l*
149×distribute-lft-out
47×associate-/l/
17×associate-*l/
15×add-cbrt-cube add-exp-log
14×tan-quot
12×associate-/r*
10×pow1
9×associate-*r*
8×flip3-- associate-/r/ flip--
6×frac-sub
5×div-inv
4×insert-posit16 add-log-exp
3×cbrt-undiv flip3-+ div-exp pow-prod-down frac-add prod-exp *-commutative cbrt-unprod flip-+
2×frac-times clear-num frac-2neg div-sub associate-*r/
Calls
4 calls:
Slowest
558.0ms
(/ (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- 1 (* (tan y) (tan z)))) (cos a))
24.0ms
(* (+ (tan y) (tan z)) (cos a))
13.0ms
(* (tan y) (tan z))
13.0ms
(* (tan y) (tan z))

series806.0ms

Calls
4 calls:
Slowest
465.0ms
(/ (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- 1 (* (tan y) (tan z)))) (cos a))
158.0ms
(* (+ (tan y) (tan z)) (cos a))
93.0ms
(* (tan y) (tan z))
90.0ms
(* (tan y) (tan z))

simplify2.4m

Calls
1324 calls:
Slowest
545.0ms
(/ (/ (sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (sqrt (- 1 (* (tan y) (tan z))))) 1)
442.0ms
(/ (/ (- (sqrt (* (+ (tan y) (tan z)) (cos a))) (sqrt (* (- 1 (* (tan y) (tan z))) (sin a)))) (- 1 (sqrt (* (tan y) (tan z))))) (cbrt (cos a)))
433.0ms
(/ (* (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))) (+ (sqrt 1) (* (sqrt (tan y)) (sqrt (tan z)))))
420.0ms
(/ (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- 1 (sqrt (* (tan y) (tan z))))) (cbrt (cos a)))
419.0ms
(/ (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- (sqrt 1) (sqrt (* (tan y) (tan z))))) (cbrt (cos a)))

prune10.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.1s

Algorithm
rewrite-expression-head
Rules
14239×*-un-lft-identity
12248×associate-*l*
10839×associate-*r*
8219×add-sqr-sqrt
5980×distribute-lft-out
4626×unswap-sqr
4140×times-frac
2510×distribute-lft-out--
1540×difference-of-squares
1226×swap-sqr
533×*-commutative
489×add-cube-cbrt
121×pow1
115×associate-/r*
96×tan-quot
81×associate-*r/
75×frac-times
60×add-cbrt-cube add-exp-log
54×associate-*l/
51×pow-prod-down
36×associate-/l*
34×prod-exp cbrt-unprod
18×flip3-+ flip-+ associate-/l/
17×associate-/r/
16×frac-sub
15×flip3-- flip--
12×pow-sqr pow-prod-up
9×cos-mult
6×pow-plus
5×cbrt-undiv div-sub div-exp
4×insert-posit16 associate--r+ add-log-exp
3×pow2
2×distribute-rgt-in sub-neg distribute-lft-in
1×clear-num frac-2neg div-inv
Calls
4 calls:
Slowest
39.3s
(/ (- (* (* (+ (* (cos y) (sin z)) (* (cos z) (sin y))) (cos a)) (+ (+ (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))) 1)) (* (* (cos z) (* (cos y) (sin a))) (- 1 (* (* (tan z) (tan y)) (* (* (tan z) (tan y)) (* (tan z) (tan y))))))) (* (cos a) (* (- 1 (* (tan y) (tan z))) (* (* (cos y) (cos z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))))))
73.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
69.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
67.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))

series1.9s

Calls
4 calls:
Slowest
1.6s
(/ (- (* (* (+ (* (cos y) (sin z)) (* (cos z) (sin y))) (cos a)) (+ (+ (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))) 1)) (* (* (cos z) (* (cos y) (sin a))) (- 1 (* (* (tan z) (tan y)) (* (* (tan z) (tan y)) (* (tan z) (tan y))))))) (* (cos a) (* (- 1 (* (tan y) (tan z))) (* (* (cos y) (cos z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))))))
106.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
105.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
104.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))