Details

Time bar (total: 43.6s)

sample329.0ms

Algorithm
intervals
Results
175.0ms129×body1280valid
51.0ms57×body640valid
47.0ms256×pre80true
9.0ms16×body320valid
7.0ms38×body80valid
6.0ms16×body160valid

simplify6.6s

Counts
1 → 1
Iterations
IterNodes
done5000
94724
81354
7446
6193
589
439
333
222
115
09

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

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))
2.8b
(tan (+ y z))

rewrite50.0ms

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
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 → 42
Calls
3 calls:
14.0ms
(+ x (- (tan (+ y z)) (tan a)))
28.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(tan (+ y z))

series499.0ms

Counts
3 → 9
Calls
3 calls:
218.0ms
(+ x (- (tan (+ y z)) (tan a)))
200.0ms
(- (tan (+ y z)) (tan a))
80.0ms
(tan (+ y z))

simplify1.2s

Counts
51 → 51
Iterations
IterNodes
done5001
31734
2475
1198
091

prune502.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

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

rewrite189.0ms

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×flip3-+ frac-add flip-+
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 diff-log div-sub div-inv
Counts
4 → 92
Calls
4 calls:
57.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
14.0ms
(* (tan y) (tan z))
15.0ms
(* (tan y) (tan z))
97.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.7s

Counts
4 → 12
Calls
4 calls:
539.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
175.0ms
(* (tan y) (tan z))
166.0ms
(* (tan y) (tan z))
859.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify3.2s

Counts
104 → 104
Iterations
IterNodes
done5001
23594
1675
0195

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.3b
(/ (log (/ (exp (* (+ (tan y) (tan z)) (cos a))) (exp (* (- 1 (* (tan y) (tan z))) (sin a))))) (* (- 1 (* (tan y) (tan z))) (cos a)))
0.3b
(exp (* (+ (tan y) (tan z)) (cos a)))
2.6b
(log (/ (exp (* (+ (tan y) (tan z)) (cos a))) (exp (* (- 1 (* (tan y) (tan z))) (sin a)))))

rewrite524.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×log-prod times-frac
12×add-exp-log
11×add-cbrt-cube
9×pow1
8×add-log-exp
4×tan-quot associate-/l*
3×div-exp associate-*r* associate-*l* associate-*l/ log-pow
2×cbrt-undiv log-div exp-to-pow rem-log-exp prod-exp associate-/r/ cbrt-unprod div-inv
1×frac-times exp-prod clear-num associate-/r* sum-log frac-2neg flip3-- div-sub pow-prod-down associate-*r/ *-commutative flip-- unswap-sqr rem-exp-log
Counts
4 → 82
Calls
4 calls:
25.0ms
(* (tan y) (tan z))
451.0ms
(/ (log (/ (exp (* (+ (tan y) (tan z)) (cos a))) (exp (* (- 1 (* (tan y) (tan z))) (sin a))))) (* (- 1 (* (tan y) (tan z))) (cos a)))
29.0ms
(exp (* (+ (tan y) (tan z)) (cos a)))
14.0ms
(log (/ (exp (* (+ (tan y) (tan z)) (cos a))) (exp (* (- 1 (* (tan y) (tan z))) (sin a)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
160.0ms
(* (tan y) (tan z))
887.0ms
(/ (log (/ (exp (* (+ (tan y) (tan z)) (cos a))) (exp (* (- 1 (* (tan y) (tan z))) (sin a))))) (* (- 1 (* (tan y) (tan z))) (cos a)))
277.0ms
(exp (* (+ (tan y) (tan z)) (cos a)))
630.0ms
(log (/ (exp (* (+ (tan y) (tan z)) (cos a))) (exp (* (- 1 (* (tan y) (tan z))) (sin a)))))

simplify1.7s

Counts
94 → 94
Iterations
IterNodes
done5001
21505
1430
0188

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize201.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))
0.3b
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))))
0.5b
(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))))
3.5b
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
171×frac-times
105×flip3-- frac-sub flip--
99×*-un-lft-identity
84×add-sqr-sqrt
63×cbrt-div
57×associate-*l/
56×times-frac
33×associate-*r/
30×pow1
24×distribute-lft-out-- difference-of-squares
20×associate-*r*
14×swap-sqr
11×add-cbrt-cube associate-*l* add-exp-log
9×add-cube-cbrt
8×distribute-lft-out
7×pow-plus pow-prod-up
6×add-log-exp
5×sub-neg
4×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
3×pow2 pow-sqr
2×pow3 *-commutative unswap-sqr
1×cbrt-prod pow1/3 diff-log rem-cbrt-cube
Counts
4 → 264
Calls
4 calls:
118.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))
1.0s
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))))
567.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))))
661.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))))

series3.3s

Counts
4 → 12
Calls
4 calls:
638.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))
1.1s
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))))
852.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))))
688.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (sin a) (cos a)))))

simplify2.0s

Counts
276 → 276
Iterations
IterNodes
done5001
11075
0376

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes1.5s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done25
125
019

end0.0ms

sample11.0s

Algorithm
intervals
Results
6.2s3899×body1280valid
2.3s1935×body640valid
1.3s8000×pre80true
389.0ms683×body320valid
193.0ms1185×body80valid
144.0ms298×body160valid