Details

Time bar (total: 51.9s)

sample423.0ms

Algorithm
intervals
Results
270.0ms124×body1280valid
68.0ms69×body640valid
33.0ms256×pre80true
11.0ms15×body320valid
9.0ms38×body80valid
5.0ms10×body160valid

simplify53.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
53.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize46.0ms

Local error

Found 3 expressions with local error:

3.1b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite46.0ms

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
25.0ms
(- (tan (+ y z)) (tan a))
10.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(tan (+ y z))

series467.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
211.0ms
(+ x (- (tan (+ y z)) (tan a)))
179.0ms
(- (tan (+ y z)) (tan a))
77.0ms
(tan (+ y z))

simplify1.6s

Counts
25 → 54
Calls
25 calls:
Slowest
507.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
174.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
163.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
150.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))
131.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))

prune626.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b
(+ (tan y) (tan z))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite192.0ms

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
100.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
52.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
31.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
549.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
498.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
163.0ms
(* (tan y) (tan z))
155.0ms
(+ (tan y) (tan z))

simplify3.7s

Counts
45 → 83
Calls
45 calls:
Slowest
447.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
355.0ms
(- (+ (/ (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)))
328.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
322.0ms
(- (+ (/ (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)))
284.0ms
(- (+ (/ (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)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.3b
(* (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)) (* (- 1 (* (tan y) (tan z))) (sin a)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×tan-quot
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
12×frac-sub
10×*-un-lft-identity add-cube-cbrt
9×flip3-- flip--
8×pow1 associate-/l/
6×associate-*r* associate-*l* add-log-exp
4×flip3-+ frac-add flip-+ insert-posit16
3×times-frac prod-exp cbrt-unprod associate-/l*
2×frac-times cbrt-undiv div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub div-inv
Counts
4 → 96
Calls
4 calls:
Slowest
106.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
46.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
27.0ms
(* (tan y) (tan z))
19.0ms
(* (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
654.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
422.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
108.0ms
(* (tan y) (tan z))
98.0ms
(* (tan y) (tan z))

simplify13.7s

Counts
77 → 108
Calls
77 calls:
Slowest
695.0ms
(- (* (* (+ (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))))
537.0ms
(* (* (cos y) (cos z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))
489.0ms
(- (* (* (+ (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))))
477.0ms
(/ (sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (cos a))
465.0ms
(* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
27×associate-*l/
14×add-sqr-sqrt
13×add-cbrt-cube tan-quot add-exp-log
12×frac-sub
10×*-un-lft-identity add-cube-cbrt
9×flip3-- flip--
8×pow1 associate-/l/
6×associate-*r* associate-*l* add-log-exp
4×flip3-+ frac-add flip-+ insert-posit16
3×times-frac prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative unswap-sqr
1×frac-times clear-num associate-/r* sub-neg frac-2neg diff-log div-sub div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
86.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
38.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))
15.0ms
(* (tan y) (tan z))
11.0ms
(* (sin y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
616.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
434.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))
117.0ms
(* (tan y) (tan z))
111.0ms
(* (sin y) (tan z))

simplify10.4s

Counts
74 → 106
Calls
74 calls:
Slowest
466.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))) (* (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
429.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (cos a) (cos a)) (cos a))))
418.0ms
(* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (+ 1 (/ (* (sin y) (tan z)) (cos y))))
388.0ms
(- (* (* (+ (pow (tan y) 3) (pow (tan z) 3)) (cos a)) (+ (* 1 1) (+ (* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y))) (* 1 (/ (* (sin y) (tan z)) (cos y)))))) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (* (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3)) (sin a))))
387.0ms
(- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y))) (* 1 (/ (* (sin y) (tan z)) (cos y)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3)) (sin a))))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes382.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample11.2s

Algorithm
intervals
Results
6.7s3933×body1280valid
2.0s1961×body640valid
1.1s8000×pre80true
493.0ms675×body320valid
411.0ms300×body160valid
249.0ms1131×body80valid