Details

Time bar (total: 43.8s)

sample537.0ms

Algorithm
intervals
Results
292.0ms118×body1280valid
134.0ms68×body640valid
32.0ms256×pre80true
25.0ms26×body320valid
11.0ms33×body80valid
7.0ms11×body160valid

simplify56.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize40.0ms

Local error

Found 3 expressions with local error:

3.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite43.0ms

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
Calls
3 calls:
Slowest
23.0ms
(- (tan (+ y z)) (tan a))
10.0ms
(+ x (- (tan (+ y z)) (tan a)))
9.0ms
(tan (+ y z))

series376.0ms

Calls
3 calls:
Slowest
152.0ms
(+ x (- (tan (+ y z)) (tan a)))
148.0ms
(- (tan (+ y z)) (tan a))
76.0ms
(tan (+ y z))

simplify1.5s

Calls
25 calls:
Slowest
455.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
134.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
129.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
126.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
102.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))

prune599.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt add-log-exp
7×tan-quot
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
4×insert-posit16
3×sum-log associate-*r* associate-*l* distribute-lft-out
2×+-commutative associate-+r+ sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- times-frac flip3-- pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-- unswap-sqr
Calls
4 calls:
Slowest
130.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
96.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms
(* (tan y) (tan z))
14.0ms
(+ (tan y) (tan z))

series1.2s

Calls
4 calls:
Slowest
515.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
433.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
141.0ms
(* (tan y) (tan z))
123.0ms
(+ (tan y) (tan z))

simplify3.8s

Calls
45 calls:
Slowest
350.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
350.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
347.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
328.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
296.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))) (/ (sin a) (cos a)))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

2.5b
(exp (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a))))
0.2b
(* (tan y) (tan z))
0.1b
(+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a)))
0.1b
(+ (tan y) (tan z))

rewrite330.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
17×add-log-exp
9×add-sqr-sqrt
7×add-cube-cbrt
6×pow1 add-cbrt-cube tan-quot add-exp-log
5×exp-prod sum-log distribute-lft-out
4×insert-posit16
3×associate-*r* associate-*l* frac-add rem-exp-log
2×+-commutative associate-+r+ associate-+r- flip3-+ diff-log flip-+ distribute-lft-out--
1×frac-times sub-neg flip3-- exp-diff exp-sum pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-- unswap-sqr
Calls
4 calls:
Slowest
204.0ms
(exp (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a))))
84.0ms
(+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a)))
26.0ms
(* (tan y) (tan z))
14.0ms
(+ (tan y) (tan z))

series1.7s

Calls
4 calls:
Slowest
735.0ms
(+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a)))
683.0ms
(exp (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a))))
123.0ms
(+ (tan y) (tan z))
118.0ms
(* (tan y) (tan z))

simplify5.0s

Calls
51 calls:
Slowest
508.0ms
(+ (* (+ (tan y) (tan z)) (+ x (tan a))) (* (- 1 (* (tan y) (tan z))) (- (* x x) (* (tan a) (tan a)))))
477.0ms
(exp (- (+ x (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))))) (/ (sin a) (cos a))))
425.0ms
(exp (- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a))))
388.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
328.0ms
(* (- 1 (* (tan y) (tan z))) (+ (* x x) (+ (* (tan a) (tan a)) (* x (tan a)))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

3.1b
(pow E (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a))))
0.2b
(* (tan y) (tan z))
0.1b
(+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a)))
0.1b
(+ (tan y) (tan z))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
11×add-log-exp
10×add-sqr-sqrt
8×add-cube-cbrt
7×pow1 add-exp-log
6×add-cbrt-cube tan-quot
5×pow-unpow distribute-lft-out
4×insert-posit16
3×sum-log unpow-prod-down associate-*r* associate-*l* frac-add
2×+-commutative associate-+r+ associate-+r- flip3-+ pow-exp flip-+ distribute-lft-out--
1×frac-times pow-to-exp unpow-prod-up e-exp-1 sub-neg pow-pow flip3-- diff-log pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-- pow-sub unswap-sqr sqr-pow
Calls
4 calls:
Slowest
58.0ms
(pow E (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a))))
50.0ms
(+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a)))
13.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.6s

Calls
4 calls:
Slowest
667.0ms
(+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a)))
657.0ms
(pow E (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a))))
132.0ms
(+ (tan y) (tan z))
112.0ms
(* (tan y) (tan z))

simplify6.0s

Calls
53 calls:
Slowest
498.0ms
(+ (* (+ (tan y) (tan z)) (+ x (tan a))) (* (- 1 (* (tan y) (tan z))) (- (* x x) (* (tan a) (tan a)))))
430.0ms
(exp (- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a))))
378.0ms
(exp (- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a))))
368.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
352.0ms
(* (- 1 (* (tan y) (tan z))) (+ (* x x) (+ (* (tan a) (tan a)) (* x (tan a)))))

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes739.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample15.5s

Algorithm
intervals
Results
8.7s3847×body1280valid
3.3s2051×body640valid
1.4s8000×pre80true
800.0ms670×body320valid
644.0ms286×body160valid
343.0ms1146×body80valid