Details

Time bar (total: 1.5m)

sample421.0ms

Algorithm
intervals
Results
237.0ms131×body1280valid
70.0ms60×body640valid
64.0ms256×pre80true
15.0ms22×body320valid
8.0ms34×body80valid
4.0ms9×body160valid

simplify64.0ms

Calls
1 calls:
Slowest
63.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize20.0ms

Local error

Found 3 expressions with local error:

4.3b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-log-exp
4×tan-quot
3×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
2×tan-sum associate-+r+ sub-neg frac-sub
1×+-commutative associate-+r- flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out-- difference-of-squares
Calls
3 calls:
Slowest
6.0ms
(- (tan (+ y z)) (tan a))
3.0ms
(+ x (- (tan (+ y z)) (tan a)))
2.0ms
(tan (+ y z))

series299.0ms

Calls
3 calls:
Slowest
116.0ms
(- (tan (+ y z)) (tan a))
116.0ms
(+ x (- (tan (+ y z)) (tan a)))
66.0ms
(tan (+ y z))

simplify905.0ms

Calls
21 calls:
Slowest
419.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
109.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
60.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
58.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
53.0ms
(+ (* 1/3 (pow y 3)) (+ z y))

prune541.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
8×add-log-exp
7×tan-quot
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
4×insert-posit16
3×associate-*r* associate-*l*
2×+-commutative associate-+r+ sub-neg flip3-+ flip-+ difference-of-squares
1×frac-times associate-+r- sum-log times-frac flip3-- diff-log pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-- distribute-lft-out distribute-lft-out--
Calls
4 calls:
Slowest
71.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
33.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
10.0ms
(* (tan y) (tan z))
8.0ms
(+ (tan y) (tan z))

series994.0ms

Calls
4 calls:
Slowest
407.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
389.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
104.0ms
(+ (tan y) (tan z))
94.0ms
(* (tan y) (tan z))

simplify2.8s

Calls
39 calls:
Slowest
366.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
320.0ms
(- (+ (/ (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)))
320.0ms
(- (+ (/ (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)))
303.0ms
(- (+ (/ (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)))
285.0ms
(- (+ (/ (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

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×*-un-lft-identity
11×add-cbrt-cube add-exp-log
8×add-cube-cbrt add-log-exp
6×pow1
5×tan-quot
4×times-frac insert-posit16
3×associate-/r* associate-*r* associate-*l*
2×cbrt-undiv div-exp associate-*l/ prod-exp cbrt-unprod difference-of-squares
1×+-commutative clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log pow-prod-down frac-add *-commutative frac-sub flip-+ div-inv flip-- distribute-lft-out associate-/l* distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
72.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
9.0ms
(/ (* (tan y) (sin z)) (cos z))
5.0ms
(* (tan y) (sin z))
4.0ms
(+ (tan y) (tan z))

series750.0ms

Calls
4 calls:
Slowest
453.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
115.0ms
(+ (tan y) (tan z))
113.0ms
(/ (* (tan y) (sin z)) (cos z))
68.0ms
(* (tan y) (sin z))

simplify2.9s

Calls
48 calls:
Slowest
288.0ms
(* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a))
274.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))
241.0ms
(- (+ (/ (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)))
238.0ms
(- (+ (/ (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)))
207.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

3.7b
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))
0.5b
(* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
0.3b
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
0.3b
(* (tan y) (sin z))

rewrite593.0ms

Algorithm
rewrite-expression-head
Rules
171×frac-times
105×tan-quot
104×flip3-- frac-sub flip--
63×cbrt-div
58×associate-*l/
33×associate-*r/
25×pow1
24×add-sqr-sqrt
15×*-un-lft-identity associate-*r*
13×add-cbrt-cube add-exp-log
10×associate-*l*
9×add-cube-cbrt
6×pow-plus pow-prod-up difference-of-squares
5×pow-prod-down prod-exp cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in insert-posit16 add-log-exp
3×pow2 times-frac *-commutative distribute-lft-out--
2×pow3
1×cbrt-prod pow1/3 rem-cbrt-cube
Calls
4 calls:
Slowest
263.0ms
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
188.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))
132.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
5.0ms
(* (tan y) (sin z))

series1.5s

Calls
4 calls:
Slowest
609.0ms
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
453.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
374.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))
59.0ms
(* (tan y) (sin z))

simplify1.0m

Calls
265 calls:
Slowest
868.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3))))
849.0ms
(* (* (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3)) (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3))) (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3)))
819.0ms
(cbrt (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))))
809.0ms
(cbrt (* (* (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a))) (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a)))) (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a)))))
772.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a)))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes280.0ms

Accuracy

0% (0.2b remaining)

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

bsearch8.0ms

end0.0ms

sample9.8s

Algorithm
intervals
Results
6.4s3906×body1280valid
1.8s2010×body640valid
582.0ms8000×pre80true
406.0ms706×body320valid
306.0ms1099×body80valid
103.0ms279×body160valid