Details

Time bar (total: 51.9s)

sample453.0ms

Algorithm
intervals
Results
205.0ms104×body1280valid
144.0ms70×body640valid
29.0ms256×pre80true
23.0ms23×body320valid
14.0ms52×body80valid
4.0ms7×body160valid

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
56.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize34.0ms

Local error

Found 3 expressions with local error:

2.9b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
2×tan-sum associate-+r+ sum-log sub-neg diff-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-+ flip3-- flip-+ flip-- difference-of-squares
Counts
3 → 45
Calls
3 calls:
Slowest
12.0ms
(- (tan (+ y z)) (tan a))
10.0ms
(+ x (- (tan (+ y z)) (tan a)))
5.0ms
(tan (+ y z))

series391.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
169.0ms
(+ x (- (tan (+ y z)) (tan a)))
164.0ms
(- (tan (+ y z)) (tan a))
58.0ms
(tan (+ y z))

simplify1.5s

Counts
25 → 54
Calls
25 calls:
Slowest
452.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
147.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
135.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
132.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
89.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))

prune674.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
14×*-un-lft-identity tan-quot
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×associate-/l/
6×frac-sub
5×flip3-- flip--
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×flip3-+ times-frac pow-prod-down frac-add *-commutative flip-+ associate-/l* unswap-sqr
2×frac-times cbrt-undiv div-exp associate-*r/ associate-/r/
1×clear-num associate-/r* frac-2neg div-sub div-inv distribute-lft-out
Counts
4 → 100
Calls
4 calls:
Slowest
62.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
22.0ms
(* (+ (tan y) (tan z)) (cos a))
14.0ms
(* (tan y) (tan z))
13.0ms
(* (tan y) (tan z))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
709.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
257.0ms
(* (+ (tan y) (tan z)) (cos a))
138.0ms
(* (tan y) (tan z))
137.0ms
(* (tan y) (tan z))

simplify10.9s

Counts
77 → 112
Calls
77 calls:
Slowest
833.0ms
(- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))
736.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
528.0ms
(- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))
478.0ms
(- (* (* (+ (pow (tan y) 3) (pow (tan z) 3)) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))
436.0ms
(* (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)))))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b
(pow (* (tan y) (tan z)) 3)
0.2b
(* (tan y) (tan z))
0.2b
(* (tan y) (tan z))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
50×pow1
44×tan-quot
23×add-cbrt-cube add-exp-log
20×frac-times pow-prod-down
14×associate-*l/ associate-*r/
13×add-sqr-sqrt
11×prod-exp cbrt-unprod
9×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
4×pow-sqr pow-prod-up insert-posit16 add-log-exp
3×cube-div pow-unpow *-commutative
2×pow-pow pow-plus pow-exp rem-cube-cbrt unswap-sqr
1×pow2 cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod swap-sqr sqr-pow
Counts
4 → 120
Calls
4 calls:
Slowest
84.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
15.0ms
(* (tan y) (tan z))
13.0ms
(* (tan y) (tan z))
10.0ms
(pow (* (tan y) (tan z)) 3)

series547.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(pow (* (tan y) (tan z)) 3)
141.0ms
(* (tan y) (tan z))
138.0ms
(* (tan y) (tan z))
127.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify7.5s

Counts
111 → 132
Calls
111 calls:
Slowest
932.0ms
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
930.0ms
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
844.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
756.0ms
(* (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
343.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (tan z) 3)
0.3b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b
(* (tan y) (tan y))
0.2b
(* (tan y) (tan z))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
53×pow1
41×tan-quot
21×add-cbrt-cube add-exp-log
19×frac-times pow-prod-down
17×add-sqr-sqrt
13×*-un-lft-identity associate-*l/ associate-*r/ add-cube-cbrt
10×prod-exp cbrt-unprod
7×associate-*r* associate-*l*
5×pow-sqr pow-prod-up
4×swap-sqr insert-posit16 add-log-exp
3×pow-unpow unpow-prod-down pow-plus cube-prod *-commutative
2×pow2 unswap-sqr
1×cube-div cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 126
Calls
4 calls:
Slowest
63.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
14.0ms
(* (tan y) (tan y))
13.0ms
(* (tan y) (tan z))
3.0ms
(pow (tan z) 3)

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
108.0ms
(* (tan y) (tan z))
48.0ms
(pow (tan z) 3)
35.0ms
(* (tan y) (tan y))

simplify5.4s

Counts
121 → 138
Calls
121 calls:
Slowest
704.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
554.0ms
(* (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
395.0ms
(+ (* 2/3 (* (pow z 2) (pow y 4))) (+ (* 2/3 (* (pow z 4) (pow y 2))) (* (pow z 2) (pow y 2))))
256.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
227.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune3.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes882.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch11.0ms

end0.0ms

sample13.6s

Algorithm
intervals
Results
8.2s3913×body1280valid
3.2s2012×body640valid
762.0ms8000×pre80true
592.0ms665×body320valid
382.0ms1132×body80valid
160.0ms278×body160valid