Details

Time bar (total: 53.6s)

sample531.0ms

Algorithm
intervals
Results
269.0ms119×body1280valid
129.0ms67×body640valid
37.0ms37×body80valid
34.0ms256×pre80true
16.0ms16×body320valid
12.0ms17×body160valid

simplify68.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
68.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 3 expressions with local error:

4.9b
(tan (+ y z))
0.1b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite42.0ms

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
23.0ms
(- (tan (+ y z)) (tan a))
10.0ms
(+ x (- (tan (+ y z)) (tan a)))
9.0ms
(tan (+ y z))

series385.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
179.0ms
(+ x (- (tan (+ y z)) (tan a)))
140.0ms
(- (tan (+ y z)) (tan a))
66.0ms
(tan (+ y z))

simplify1.5s

Counts
25 → 54
Calls
25 calls:
Slowest
458.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
145.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))
116.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
116.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
103.0ms
(+ (* 1/3 (pow y 3)) (+ z y))

prune594.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
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)))

rewrite199.0ms

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
97.0ms
(+ 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))
14.0ms
(* (tan y) (tan z))
11.0ms
(+ (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
578.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
470.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
124.0ms
(* (tan y) (tan z))
109.0ms
(+ (tan y) (tan z))

simplify3.6s

Counts
45 → 83
Calls
45 calls:
Slowest
465.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
347.0ms
(- (+ (/ (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)))
325.0ms
(- (+ (/ (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)))
323.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
321.0ms
(- (+ (/ (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

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

8.4b
(cbrt (* (tan y) (tan z)))
8.4b
(cbrt (* (tan y) (tan z)))
8.4b
(cbrt (* (tan y) (tan z)))
0.4b
(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
44×tan-quot
33×cbrt-div
20×frac-times
14×associate-*l/ associate-*r/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 86
Calls
4 calls:
Slowest
82.0ms
(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
13.0ms
(cbrt (* (tan y) (tan z)))
10.0ms
(cbrt (* (tan y) (tan z)))
8.0ms
(cbrt (* (tan y) (tan z)))

series890.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
234.0ms
(cbrt (* (tan y) (tan z)))
213.0ms
(cbrt (* (tan y) (tan z)))
174.0ms
(cbrt (* (tan y) (tan z)))

simplify4.0s

Counts
78 → 98
Calls
78 calls:
Slowest
564.0ms
(+ (exp (* 1/3 (+ (log z) (log y)))) (+ (* 1/9 (* (exp (* 1/3 (+ (log z) (log y)))) (pow y 2))) (* 1/9 (* (exp (* 1/3 (+ (log z) (log y)))) (pow z 2)))))
316.0ms
(+ (exp (* 1/3 (+ (* 2 (log z)) (* 2 (log y))))) (+ (* 2/9 (* (exp (* 1/3 (+ (* 2 (log z)) (* 2 (log y))))) (pow z 2))) (* 2/9 (* (exp (* 1/3 (+ (* 2 (log z)) (* 2 (log y))))) (pow y 2)))))
314.0ms
(pow (/ (* (sin z) (sin y)) (* (cos y) (cos z))) 1/3)
297.0ms
(pow (/ (* (sin z) (sin y)) (* (cos y) (cos z))) 1/3)
296.0ms
(pow (/ (* (sin z) (sin y)) (* (cos y) (cos z))) 1/3)

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

1.5b
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.4b
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
106×*-un-lft-identity
80×times-frac
70×add-sqr-sqrt
54×add-cube-cbrt
24×swap-sqr associate-*r* associate-*l*
23×distribute-lft-out
22×add-cbrt-cube add-exp-log
21×tan-quot
15×pow1
11×associate-/r/ associate-/l/
9×frac-times associate-*l/ associate-*r/ frac-sub
6×prod-exp cbrt-unprod unswap-sqr
5×cbrt-undiv flip3-- div-exp div-inv flip-- difference-of-squares
4×associate-/r* insert-posit16 associate-/l* add-log-exp
3×pow-prod-down *-commutative
1×pow2 clear-num frac-2neg flip3-+ pow-plus div-sub frac-add pow-sqr pow-prod-up flip-+
Counts
4 → 185
Calls
4 calls:
Slowest
136.0ms
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
74.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
28.0ms
(* (tan y) (tan z))
17.0ms
(* (tan y) (tan z))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
261.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
109.0ms
(* (tan y) (tan z))
106.0ms
(* (tan y) (tan z))

simplify21.4s

Counts
205 → 197
Calls
205 calls:
Slowest
720.0ms
(* (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))
486.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
457.0ms
(* (* (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))
450.0ms
(/ (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
436.0ms
(/ (* (* (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a)))) (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a)))) (* (* (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes357.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample11.1s

Algorithm
intervals
Results
6.1s3841×body1280valid
3.3s2074×body640valid
632.0ms8000×pre80true
434.0ms667×body320valid
253.0ms1126×body80valid
168.0ms292×body160valid