Details

Time bar (total: 15.8s)

sample332.0ms

Algorithm
intervals
Results
156.0ms118×body1280valid
64.0ms23×body320valid
54.0ms72×body640valid
16.0ms256×pre80true
6.0ms31×body80valid
4.0ms12×body160valid

simplify157.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize16.0ms

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))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
2×sub-neg tan-sum associate-+r+ 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 → 42
Calls
3 calls:
16.0ms
(+ x (- (tan (+ y z)) (tan a)))
41.0ms
(- (tan (+ y z)) (tan a))
14.0ms
(tan (+ y z))

series501.0ms

Counts
3 → 9
Calls
3 calls:
227.0ms
(+ x (- (tan (+ y z)) (tan a)))
187.0ms
(- (tan (+ y z)) (tan a))
85.0ms
(tan (+ y z))

simplify3.4s

Counts
51 → 51
Iterations

Useful iterations: 3 (292.0ms)

IterNodesCost
091627
1196590
2453572
31243570
44659570
done5000570

prune291.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
11×add-log-exp
8×add-exp-log add-cbrt-cube
7×tan-quot
6×pow1 distribute-lft-out
4×associate-/l*
3×associate-*r* associate-*l* associate-/r* associate-/l/
2×sub-neg associate-+r+ flip3-- flip3-+ diff-log sum-log associate-/r/ flip-- 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 div-inv unswap-sqr
Counts
4 → 90
Calls
4 calls:
49.0ms
(/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y))))
118.0ms
(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
183.0ms
(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
17.0ms
(* (tan z) (tan y))

series1.7s

Counts
4 → 12
Calls
4 calls:
327.0ms
(/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y))))
635.0ms
(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
632.0ms
(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
139.0ms
(* (tan z) (tan y))

simplify2.5s

Counts
102 → 102
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01892099
14501986
212331912
334981900
done50011900

prune491.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
0.2b
(* (tan z) (tan y))
0.2b
(* (tan z) (tan y))
0.2b
(* (tan z) (tan y))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
49×pow1
44×tan-quot
22×add-exp-log add-cbrt-cube
20×frac-times pow-prod-down
16×add-sqr-sqrt
14×associate-*r/ associate-*l/
11×prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×pow-sqr *-commutative pow-prod-up add-log-exp
3×unswap-sqr
2×pow-plus
1×pow2 swap-sqr
Counts
4 → 112
Calls
4 calls:
84.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
16.0ms
(* (tan z) (tan y))
21.0ms
(* (tan z) (tan y))
17.0ms
(* (tan z) (tan y))

series528.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
117.0ms
(* (tan z) (tan y))
129.0ms
(* (tan z) (tan y))
114.0ms
(* (tan z) (tan y))

simplify2.3s

Counts
124 → 124
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01161312
13051231
210291047
337511017
done50001017

prune412.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (tan z) (tan y)) (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
0.2b
(* (tan z) (tan y))
0.2b
(* (tan z) (tan y))
0.3b
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
29×prod-exp cbrt-unprod
16×tan-quot
13×pow1 add-sqr-sqrt
12×cbrt-undiv div-exp associate-*r*
9×add-cube-cbrt *-un-lft-identity
7×frac-times associate-*l* associate-*l/
5×associate-*r/ pow-prod-down
4×add-log-exp
3×*-commutative
2×times-frac associate-/r/ cos-mult div-inv unswap-sqr
1×frac-2neg clear-num associate-/r* associate-/l/ sin-mult associate-/l*
Counts
4 → 109
Calls
4 calls:
65.0ms
(* (* (tan z) (tan y)) (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
16.0ms
(* (tan z) (tan y))
16.0ms
(* (tan z) (tan y))
28.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
245.0ms
(* (* (tan z) (tan y)) (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
105.0ms
(* (tan z) (tan y))
105.0ms
(* (tan z) (tan y))
111.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify1.1s

Counts
121 → 121
Iterations

Useful iterations: 2 (366.0ms)

IterNodesCost
01692092
14821982
222881499
done50011499

prune739.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes6.0ms