Details

Time bar (total: 38.3s)

sample417.0ms

Algorithm
intervals
Results
252.0ms137×body1280valid
61.0ms61×body640valid
22.0ms256×pre80true
14.0ms20×body320valid
6.0ms30×body80valid
3.0ms8×body160valid

simplify6.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
1159
2229
3339
4399
5899
61939
74519
813809
948379
done50019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.2b
(- (tan (+ y z)) (tan a))
3.0b
(tan (+ y z))

rewrite47.0ms

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×pow1 add-exp-log expm1-log1p-u fma-def fma-neg add-cbrt-cube log1p-expm1-u
2×sub-neg tan-sum diff-log sum-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 72
Calls
3 calls:
18.0ms
(+ x (- (tan (+ y z)) (tan a)))
19.0ms
(- (tan (+ y z)) (tan a))
7.0ms
(tan (+ y z))

series486.0ms

Counts
3 → 9
Calls
3 calls:
178.0ms
(+ x (- (tan (+ y z)) (tan a)))
209.0ms
(- (tan (+ y z)) (tan a))
98.0ms
(tan (+ y z))

simplify829.0ms

Counts
81 → 81
Iterations

Useful iterations: done (825.0ms)

IterNodesCost
01281195
12831011
21003882
done5000795

prune319.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (tan y) (tan z)) (cos a))
0.2b
(* (tan y) (tan z))
0.2b
(* (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)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
14×tan-quot *-un-lft-identity
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×associate-/l/
6×frac-sub
5×flip3-- flip--
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×flip3-+ times-frac pow-prod-down frac-add *-commutative flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp associate-/r/
1×frac-2neg div-sub clear-num associate-/r* div-inv distribute-lft-out
Counts
4 → 104
Calls
4 calls:
37.0ms
(* (+ (tan y) (tan z)) (cos a))
17.0ms
(* (tan y) (tan z))
17.0ms
(* (tan y) (tan z))
74.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.3s

Counts
4 → 12
Calls
4 calls:
247.0ms
(* (+ (tan y) (tan z)) (cos a))
164.0ms
(* (tan y) (tan z))
169.0ms
(* (tan y) (tan z))
746.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify2.0s

Counts
116 → 116
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02012242
16322134
234751770
done50001766

prune807.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a))))
0.3b
(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
0.5b
(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
0.7b
(/ (- (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a)))))

rewrite853.0ms

Algorithm
rewrite-expression-head
Rules
475×associate-*l/
145×frac-times
144×tan-quot
122×associate-/l/
120×frac-sub
99×flip3-- flip--
87×pow1
72×flip3-+ frac-add flip-+
59×associate-*r/
42×add-exp-log add-cbrt-cube
37×pow-prod-down
22×prod-exp cbrt-unprod
8×pow-sqr pow-prod-up
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×associate-*r*
4×expm1-log1p-u times-frac pow-plus log1p-expm1-u associate-/l* add-log-exp
3×cbrt-undiv div-exp associate-*l* *-commutative
2×pow2 swap-sqr associate-/r/ fma-udef difference-of-squares
1×distribute-rgt-in frac-2neg distribute-lft-in div-sub clear-num associate-/r* div-inv
Counts
4 → 271
Calls
4 calls:
75.0ms
(* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a))))
105.0ms
(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
143.0ms
(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
479.0ms
(/ (- (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a)))))

series3.8s

Counts
4 → 12
Calls
4 calls:
850.0ms
(* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a))))
310.0ms
(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
278.0ms
(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
2.4s
(/ (- (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a)))))

simplify1.6s

Counts
283 → 283
Iterations

Useful iterations: done (1.6s)

IterNodesCost
045015100
1184613659
done500112336

prune3.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z)))
0.3b
(/ (* (* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z))) (cos a)) (* (cos y) (cos z)))
0.3b
(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
0.7b
(/ (- (/ (* (* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z))) (cos a)) (* (cos y) (cos z))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a)))))

rewrite715.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log add-cbrt-cube
48×pow1
35×associate-*l/
30×prod-exp cbrt-unprod
20×pow-prod-down
14×flip3-- flip--
13×associate-/l/
11×cbrt-undiv div-exp
10×associate-*r/
9×add-sqr-sqrt *-un-lft-identity
8×frac-times frac-sub
7×add-cube-cbrt
5×times-frac associate-*r* associate-/l*
4×tan-quot expm1-log1p-u pow-sqr pow-prod-up log1p-expm1-u add-log-exp
3×associate-/r/
2×frac-2neg flip3-+ pow-plus associate-*l* frac-add clear-num associate-/r* *-commutative flip-+ div-inv difference-of-squares
1×pow2 distribute-rgt-in distribute-lft-in div-sub swap-sqr cos-mult distribute-lft-out
Counts
4 → 145
Calls
4 calls:
48.0ms
(* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z)))
130.0ms
(/ (* (* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z))) (cos a)) (* (cos y) (cos z)))
82.0ms
(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
448.0ms
(/ (- (/ (* (* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z))) (cos a)) (* (cos y) (cos z))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a)))))

series3.1s

Counts
4 → 12
Calls
4 calls:
330.0ms
(* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z)))
458.0ms
(/ (* (* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z))) (cos a)) (* (cos y) (cos z)))
202.0ms
(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
2.1s
(/ (- (/ (* (* (* (cos a) (fma (sin y) (cos z) (* (cos y) (sin z)))) (+ (tan y) (tan z))) (cos a)) (* (cos y) (cos z))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (- 1 (* (tan y) (tan z))) (sin a)))))

simplify514.0ms

Counts
157 → 157
Iterations

Useful iterations: done (507.0ms)

IterNodesCost
03537855
112817484
done50006108

prune1.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes530.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01832
12632
done2632

end0.0ms

sample9.6s

Algorithm
intervals
Results
6.3s3903×body1280valid
1.4s2009×body640valid
624.0ms8000×pre80true
360.0ms690×body320valid
164.0ms285×body160valid
149.0ms1113×body80valid