Details

Time bar (total: 41.1s)

sample442.0ms

Algorithm
intervals
Results
260.0ms132×body1280valid
97.0ms61×body640valid
26.0ms256×pre80true
16.0ms21×body320valid
9.0ms35×body80valid
4.0ms7×body160valid

simplify43.0ms

Calls
1 calls:
Slowest
42.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize33.0ms

Local error

Found 3 expressions with local error:

2.8b
(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))

series400.0ms

Calls
3 calls:
Slowest
173.0ms
(+ x (- (tan (+ y z)) (tan a)))
167.0ms
(- (tan (+ y z)) (tan a))
60.0ms
(tan (+ y z))

simplify906.0ms

Calls
21 calls:
Slowest
398.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
99.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
67.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
57.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
45.0ms
(/ (exp (tan (+ y z))) (exp (tan a)))

prune521.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
20×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
8×add-cbrt-cube add-exp-log
7×tan-quot
6×pow1 add-log-exp
4×insert-posit16 distribute-lft-out associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×associate-+r+ sub-neg flip3-+ flip3-- associate-/r/ flip-+ flip-- difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num associate-+r- frac-2neg diff-log div-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out--
Calls
4 calls:
Slowest
40.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
31.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
25.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
5.0ms
(* (tan y) (tan z))

series1.2s

Calls
4 calls:
Slowest
451.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
412.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
232.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
101.0ms
(* (tan y) (tan z))

simplify4.4s

Calls
71 calls:
Slowest
484.0ms
(/ (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))))
345.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
304.0ms
(- (+ (/ (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)))
293.0ms
(- (+ (/ (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)))
272.0ms
(- (+ (/ (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: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
0.3b
(* (tan z) (tan z))
0.3b
(* (tan y) (tan y))
0.3b
(* (tan y) (tan z))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
42×tan-quot
16×pow1
15×frac-times add-cbrt-cube add-exp-log
12×add-sqr-sqrt *-un-lft-identity associate-*r/ frac-sub add-cube-cbrt
11×associate-*l/ associate-/r/ associate-/l/
9×associate-*r* associate-*l*
8×flip3-- flip--
4×times-frac prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×pow-prod-down *-commutative
2×pow2 cbrt-undiv pow-plus div-exp pow-prod-up difference-of-squares
1×clear-num associate-/r* frac-2neg div-sub div-inv
Calls
4 calls:
Slowest
30.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
9.0ms
(* (tan z) (tan z))
8.0ms
(* (tan y) (tan y))
4.0ms
(* (tan y) (tan z))

series624.0ms

Calls
4 calls:
Slowest
413.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
117.0ms
(* (tan y) (tan z))
48.0ms
(* (tan z) (tan z))
45.0ms
(* (tan y) (tan y))

simplify8.1s

Calls
93 calls:
Slowest
733.0ms
(/ (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (* (tan y) (tan y)) (* (tan z) (tan z)))) (- (* (tan y) (tan y)) (* (tan z) (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)))))
590.0ms
(/ (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (* (tan y) (tan y)) (* (tan z) (tan z)))) (- (* (tan y) (tan y)) (* (tan z) (tan z)))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z)))))
513.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
506.0ms
(/ (- (/ (pow (sin y) 2) (pow (cos y) 2)) (/ (pow (sin z) 2) (pow (cos z) 2))) (* (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))) (- (/ (sin y) (cos y)) (/ (sin z) (cos z)))))
486.0ms
(/ (- (/ (pow (sin y) 2) (pow (cos y) 2)) (/ (pow (sin z) 2) (pow (cos z) 2))) (* (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))) (- (/ (sin y) (cos y)) (/ (sin z) (cos z)))))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

16.1b
(log (* (tan y) (tan y)))
3.5b
(/ (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
1.5b
(exp (log (* (tan y) (tan y))))
0.3b
(* (tan z) (tan z))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
42×tan-quot
21×pow1
15×frac-times log-div
14×add-exp-log
12×exp-diff associate-*r/ frac-sub
11×add-sqr-sqrt add-cbrt-cube associate-*l/ associate-/r/ associate-/l/
10×log-pow
9×*-un-lft-identity add-cube-cbrt
8×exp-prod flip3-- flip--
5×times-frac associate-/l*
4×log-prod insert-posit16 add-log-exp difference-of-squares
3×pow2 pow-plus associate-*r* associate-*l* exp-sum pow-prod-down prod-exp pow-prod-up
2×cbrt-undiv div-exp rem-log-exp cbrt-unprod
1×clear-num associate-/r* frac-2neg div-sub *-commutative div-inv rem-exp-log
Calls
4 calls:
Slowest
99.0ms
(/ (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
10.0ms
(exp (log (* (tan y) (tan y))))
7.0ms
(log (* (tan y) (tan y)))
4.0ms
(* (tan z) (tan z))

series638.0ms

Calls
4 calls:
Slowest
465.0ms
(/ (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
97.0ms
(log (* (tan y) (tan y)))
42.0ms
(exp (log (* (tan y) (tan y))))
35.0ms
(* (tan z) (tan z))

simplify7.1s

Calls
90 calls:
Slowest
697.0ms
(/ (* (* (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z)))) (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z)))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z)))))
495.0ms
(/ (- (/ (pow (sin y) 2) (pow (cos y) 2)) (/ (pow (sin z) 2) (pow (cos z) 2))) (* (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))) (- (/ (sin y) (cos y)) (/ (sin z) (cos z)))))
427.0ms
(/ (* (* (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z)))) (- (exp (log (* (tan y) (tan y)))) (* (tan z) (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)))))
415.0ms
(/ (- (/ (pow (sin y) 2) (pow (cos y) 2)) (/ (pow (sin z) 2) (pow (cos z) 2))) (* (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))) (- (/ (sin y) (cos y)) (/ (sin z) (cos z)))))
349.0ms
(/ (exp (log (* (tan y) (tan y)))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes345.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample10.7s

Algorithm
intervals
Results
6.6s3952×body1280valid
2.0s1973×body640valid
994.0ms8000×pre80true
462.0ms669×body320valid
349.0ms1094×body80valid
143.0ms312×body160valid