Details

Time bar (total: 46.6s)

sample419.0ms

Algorithm
intervals
Results
232.0ms124×body1280valid
106.0ms57×body640valid
24.0ms256×pre80true
17.0ms51×body80valid
15.0ms21×body320valid
2.0ms3×body160valid

simplify42.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
41.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize26.0ms

Local error

Found 3 expressions with local error:

2.8b
(tan (+ y z))
0.1b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite56.0ms

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
26.0ms
(- (tan (+ y z)) (tan a))
22.0ms
(+ x (- (tan (+ y z)) (tan a)))
7.0ms
(tan (+ y z))

series402.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
172.0ms
(+ x (- (tan (+ y z)) (tan a)))
169.0ms
(- (tan (+ y z)) (tan a))
61.0ms
(tan (+ y z))

simplify1.5s

Counts
25 → 54
Calls
25 calls:
Slowest
404.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
152.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
129.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
122.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
104.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))

prune652.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

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
Counts
4 → 71
Calls
4 calls:
Slowest
127.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
64.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
19.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
528.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
466.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
138.0ms
(+ (tan y) (tan z))
129.0ms
(* (tan y) (tan z))

simplify4.0s

Counts
45 → 83
Calls
45 calls:
Slowest
442.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
375.0ms
(- (+ (/ (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)))
340.0ms
(- (+ (/ (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)))
326.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
316.0ms
(- (+ (/ (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)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite502.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
13×*-un-lft-identity
11×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp insert-posit16
3×sum-log associate-*r* associate-*l* distribute-lft-out
2×+-commutative associate-+r+ flip3-+ tan-quot flip-+ sin-mult
1×clear-num associate-+r- associate-/r* sub-neg frac-2neg times-frac diff-log pow-prod-down frac-add associate-/r/ cos-mult *-commutative div-inv associate-/l* distribute-lft-out-- unswap-sqr associate-/l/
Counts
4 → 76
Calls
4 calls:
Slowest
448.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))) (tan a)))
27.0ms
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))
18.0ms
(* (sin z) (sin y))
7.0ms
(+ (tan y) (tan z))

series864.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
521.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))) (tan a)))
144.0ms
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))
140.0ms
(+ (tan y) (tan z))
59.0ms
(* (sin z) (sin y))

simplify7.0s

Counts
47 → 88
Calls
47 calls:
Slowest
1.0s
(/ (* (* (* (sin z) (sin y)) (* (sin z) (sin y))) (* (sin z) (sin y))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))
827.0ms
(/ (* (* (* (sin z) (sin z)) (sin z)) (* (* (sin y) (sin y)) (sin y))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))
734.0ms
(/ (* (* (* (sin z) (sin y)) (* (sin z) (sin y))) (* (sin z) (sin y))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))
549.0ms
(/ (* (* (* (sin z) (sin z)) (sin z)) (* (* (sin y) (sin y)) (sin y))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))
438.0ms
(* (exp x) (/ (exp (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (exp (tan a))))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
0.3b
(* (tan y) (tan y))
0.3b
(* (tan z) (tan z))
0.2b
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
34×tan-quot
33×*-un-lft-identity
23×add-cube-cbrt
22×add-cbrt-cube add-exp-log
21×times-frac
18×pow1
12×associate-/l/
11×difference-of-squares
10×frac-sub
8×frac-times associate-*l/ associate-*r/
6×associate-/r* swap-sqr associate-*r* associate-*l* prod-exp cbrt-unprod
5×cbrt-undiv div-exp associate-/l* distribute-lft-out--
4×associate-/r/ insert-posit16 add-log-exp
2×pow2 clear-num frac-2neg pow-plus flip3-- pow-prod-down pow-sqr *-commutative pow-prod-up div-inv flip-- unswap-sqr
1×div-sub cos-mult sin-mult
Counts
4 → 139
Calls
4 calls:
Slowest
79.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
24.0ms
(* (tan z) (tan z))
17.0ms
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))
14.0ms
(* (tan y) (tan y))

series438.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
245.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
119.0ms
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))
38.0ms
(* (tan y) (tan y))
35.0ms
(* (tan z) (tan z))

simplify11.5s

Counts
140 → 151
Calls
140 calls:
Slowest
845.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
706.0ms
(/ (* (* (* (sin z) (sin y)) (* (sin z) (sin y))) (* (sin z) (sin y))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))
574.0ms
(/ (* (* (* (sin z) (sin z)) (sin z)) (* (* (sin y) (sin y)) (sin y))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))
535.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
487.0ms
(/ (* (* (* (sin z) (sin y)) (* (sin z) (sin y))) (* (sin z) (sin y))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes444.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample11.9s

Algorithm
intervals
Results
6.7s3903×body1280valid
2.7s1954×body640valid
997.0ms8000×pre80true
726.0ms729×body320valid
255.0ms1124×body80valid
233.0ms290×body160valid