Details

Time bar (total: 1.1m)

sample403.0ms

Algorithm
intervals
Results
217.0ms120×body1280valid
65.0ms66×body640valid
42.0ms33×body80valid
30.0ms256×pre80true
16.0ms24×body320valid
5.0ms13×body160valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
342015
331949
321871
311805
301727
291661
281583
271517
261439
251373
241295
231229
221151
211085
201007
19941
18863
17797
16719
15653
14575
13510
12430
11354
10254
9186
8103
771
661
546
435
329
222
115
09

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))
2.8b
(tan (+ y z))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
18×prod-diff
17×add-cube-cbrt
11×associate-+r+
10×add-log-exp
4×tan-quot
3×expm1-log1p-u pow1 fma-def add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×tan-sum 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 → 75
Calls
3 calls:
17.0ms
(+ x (- (tan (+ y z)) (tan a)))
22.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(tan (+ y z))

series382.0ms

Counts
3 → 9
Calls
3 calls:
158.0ms
(+ x (- (tan (+ y z)) (tan a)))
148.0ms
(- (tan (+ y z)) (tan a))
76.0ms
(tan (+ y z))

simplify596.0ms

Counts
84 → 84
Iterations
IterNodes
32108
2651
1286
0131

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize92.0ms

Local error

Found 4 expressions with local error:

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

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×expm1-log1p-u flip3-+ frac-add flip-+ insert-posit16 log1p-expm1-u
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 fma-neg diff-log div-sub prod-diff div-inv
Counts
4 → 106
Calls
4 calls:
68.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
91.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
20.0ms
(* (tan y) (tan z))
17.0ms
(* (tan y) (tan z))

series1.7s

Counts
4 → 12
Calls
4 calls:
510.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
863.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
154.0ms
(* (tan y) (tan z))
182.0ms
(* (tan y) (tan z))

simplify1.1s

Counts
118 → 118
Iterations
IterNodes
22923
1703
0209

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize150.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan z) (tan z))
0.3b
(* (tan y) (tan y))
0.3b
(* (- (tan y) (tan z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
2.3b
(/ (- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (- (tan y) (tan z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (- (tan y) (tan z)) (+ 1 (* (tan y) (tan z)))))

rewrite913.0ms

Algorithm
rewrite-expression-head
Rules
1099×associate-*l/
1038×tan-quot
801×frac-sub
664×frac-times
391×associate-/l/
300×associate-*r/
289×flip3-- flip--
136×flip3-+ flip-+
23×pow1
21×add-sqr-sqrt
18×add-cbrt-cube add-exp-log
17×*-un-lft-identity
15×add-cube-cbrt
11×associate-*l* associate-/r/
7×associate-*r*
6×swap-sqr prod-exp cbrt-unprod
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u sub-div add-log-exp
3×times-frac *-commutative associate-/l*
2×pow2 cbrt-undiv pow-plus div-exp pow-sqr pow-prod-up unswap-sqr
1×clear-num associate-/r* frac-2neg div-sub div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 523
Calls
4 calls:
18.0ms
(* (tan z) (tan z))
21.0ms
(* (tan y) (tan y))
215.0ms
(* (- (tan y) (tan z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
605.0ms
(/ (- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (- (tan y) (tan z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (- (tan y) (tan z)) (+ 1 (* (tan y) (tan z)))))

series2.4s

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (tan z) (tan z))
47.0ms
(* (tan y) (tan y))
480.0ms
(* (- (tan y) (tan z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
1.8s
(/ (- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (- (tan y) (tan z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (- (tan y) (tan z)) (+ 1 (* (tan y) (tan z)))))

simplify2.6s

Counts
535 → 535
Iterations
IterNodes
13535
0776

prune17.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan z) (tan z))
0.3b
(* (tan y) (tan y))
0.3b
(* (- (tan y) (tan z)) (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))
2.3b
(/ (- (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (cos a) (+ (* (tan y) (tan z)) 1))) (* (- (tan y) (tan z)) (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))) (* (- (tan y) (tan z)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))

rewrite497.0ms

Algorithm
rewrite-expression-head
Rules
1038×tan-quot
852×associate-*r/
801×frac-sub
664×frac-times
444×associate-*l/
391×associate-/l/
293×flip3-- flip--
132×flip3-+ flip-+
25×add-sqr-sqrt
23×pow1
21×*-un-lft-identity
20×distribute-rgt-in distribute-lft-in
19×add-cube-cbrt
18×add-cbrt-cube add-exp-log
12×prod-diff
11×associate-*l* associate-/r/
7×associate-*r*
6×swap-sqr prod-exp cbrt-unprod
5×pow-prod-down
4×expm1-log1p-u sub-neg insert-posit16 log1p-expm1-u sub-div add-log-exp
3×times-frac *-commutative associate-/l*
2×pow2 cbrt-undiv pow-plus div-exp pow-sqr pow-prod-up unswap-sqr
1×clear-num associate-/r* frac-2neg div-sub div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 543
Calls
4 calls:
16.0ms
(* (tan z) (tan z))
17.0ms
(* (tan y) (tan y))
65.0ms
(* (- (tan y) (tan z)) (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))
370.0ms
(/ (- (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (cos a) (+ (* (tan y) (tan z)) 1))) (* (- (tan y) (tan z)) (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))) (* (- (tan y) (tan z)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (tan z) (tan z))
42.0ms
(* (tan y) (tan y))
383.0ms
(* (- (tan y) (tan z)) (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))
1.6s
(/ (- (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (cos a) (+ (* (tan y) (tan z)) 1))) (* (- (tan y) (tan z)) (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))) (* (- (tan y) (tan z)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))))

simplify1.8s

Counts
555 → 555
Iterations
IterNodes
13558
0812

prune14.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes979.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
231
131
022

end0.0ms

sample11.0s

Algorithm
intervals
Results
6.1s3899×body1280valid
3.0s1978×body640valid
670.0ms8000×pre80true
531.0ms698×body320valid
200.0ms1120×body80valid
190.0ms305×body160valid