Details

Time bar (total: 53.7s)

sample420.0ms

Algorithm
intervals
Results
187.0ms112×body1280valid
111.0ms73×body640valid
55.0ms256×pre80true
14.0ms17×body320valid
12.0ms48×body80valid
3.0ms6×body160valid

simplify80.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
80.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize29.0ms

Local error

Found 3 expressions with local error:

3.9b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite29.0ms

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))
11.0ms
(+ x (- (tan (+ y z)) (tan a)))
5.0ms
(tan (+ y z))

series381.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
146.0ms
(+ x (- (tan (+ y z)) (tan a)))
135.0ms
(- (tan (+ y z)) (tan a))
99.0ms
(tan (+ y z))

simplify1.8s

Counts
25 → 54
Calls
25 calls:
Slowest
803.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
175.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
163.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
104.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
80.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune648.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

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

rewrite246.0ms

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
126.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
77.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
27.0ms
(* (tan y) (tan z))
14.0ms
(+ (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
546.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
525.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
140.0ms
(* (tan y) (tan z))
124.0ms
(+ (tan y) (tan z))

simplify3.4s

Counts
45 → 83
Calls
45 calls:
Slowest
390.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
294.0ms
(- (+ (/ (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)))
287.0ms
(- (+ (/ (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)))
279.0ms
(- (+ (/ (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)))
271.0ms
(- (+ (/ (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)))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))
0.2b
(* (tan y) (tan z))
0.2b
(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b
(* (cos y) (sin z))

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×add-cube-cbrt
9×add-log-exp
8×pow1
6×associate-*r* associate-*l*
4×tan-quot insert-posit16
3×times-frac prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv associate-+r+ sum-log flip3-+ div-exp pow-prod-down *-commutative flip-+ distribute-lft-out unswap-sqr associate-/l/
1×frac-times +-commutative clear-num associate-+r- associate-/r* sub-neg frac-2neg diff-log associate-*l/ associate-*r/ associate-/r/ cos-mult div-inv distribute-lft-out--
Counts
4 → 84
Calls
4 calls:
Slowest
199.0ms
(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
71.0ms
(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))
20.0ms
(* (cos y) (sin z))
14.0ms
(* (tan y) (tan z))

series924.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
506.0ms
(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
214.0ms
(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))
124.0ms
(* (tan y) (tan z))
80.0ms
(* (cos y) (sin z))

simplify5.5s

Counts
58 → 96
Calls
58 calls:
Slowest
473.0ms
(* (exp x) (/ (exp (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z))))) (exp (tan a))))
459.0ms
(* (exp x) (exp (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))))
386.0ms
(- (* (* (sin y) (cos z)) (* (sin y) (cos z))) (* (* (cos y) (sin z)) (* (cos y) (sin z))))
383.0ms
(/ (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (+ (* (sin y) (cos z)) (* (cos y) (sin z)))) (+ (* (sin y) (cos z)) (* (cos y) (sin z)))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))
374.0ms
(/ (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (+ (* (sin y) (cos z)) (* (cos y) (sin z)))) (+ (* (sin y) (cos z)) (* (cos y) (sin z)))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize94.0ms

Local error

Found 4 expressions with local error:

19.5b
(cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))))
0.4b
(* (* (cos y) (sin z)) (* (cos y) (sin z)))
0.3b
(/ (+ (* (sin y) (cos z)) (cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))))) (* (cos y) (cos z)))
0.3b
(* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z)))

rewrite473.0ms

Algorithm
rewrite-expression-head
Rules
198×pow1
86×pow-prod-down
62×add-cbrt-cube add-exp-log
40×prod-exp cbrt-unprod
38×pow-prod-up
19×pow-plus
16×pow-sqr
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow2 insert-posit16 add-log-exp
3×times-frac associate-/l*
2×cbrt-undiv div-exp associate-*r* associate-*l* pow3 *-commutative associate-/l/
1×cbrt-prod clear-num associate-/r* frac-2neg flip3-+ pow1/3 swap-sqr associate-/r/ cos-mult rem-cbrt-cube flip-+ div-inv
Counts
4 → 146
Calls
4 calls:
Slowest
139.0ms
(* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z)))
139.0ms
(cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))))
115.0ms
(/ (+ (* (sin y) (cos z)) (cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))))) (* (cos y) (cos z)))
74.0ms
(* (* (cos y) (sin z)) (* (cos y) (sin z)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
244.0ms
(/ (+ (* (sin y) (cos z)) (cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))))) (* (cos y) (cos z)))
78.0ms
(* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z)))
73.0ms
(* (* (cos y) (sin z)) (* (cos y) (sin z)))
63.0ms
(cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))))

simplify15.5s

Counts
151 → 158
Calls
151 calls:
Slowest
828.0ms
(* (* (* (* (cos y) (cos y)) (cos y)) (* (* (sin z) (sin z)) (sin z))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (sin z) (sin z)) (sin z))))
823.0ms
(* (* (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))) (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z)))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (sin z) (sin z)) (sin z))))
785.0ms
(* (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))) (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))))
453.0ms
(* (* (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (sin z) (sin z)) (sin z)))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (sin z) (sin z)) (sin z))))
450.0ms
(/ (* (* (+ (* (sin y) (cos z)) (cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z))))) (+ (* (sin y) (cos z)) (cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z)))))) (+ (* (sin y) (cos z)) (cbrt (* (* (* (cos y) (sin z)) (* (cos y) (sin z))) (* (cos y) (sin z)))))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))

prune3.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes633.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample14.7s

Algorithm
intervals
Results
9.0s3844×body1280valid
3.2s2091×body640valid
949.0ms8000×pre80true
560.0ms631×body320valid
360.0ms1153×body80valid
228.0ms281×body160valid