Details

Time bar (total: 30.7s)

sample339.0ms

Algorithm
intervals
Results
175.0ms137×body1280valid
85.0ms61×body640valid
16.0ms256×pre80true
11.0ms20×body320valid
6.0ms30×body80valid
3.0ms8×body160valid

simplify6.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize13.0ms

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))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
2×sub-neg tan-sum associate-+r+ 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 → 42
Calls
3 calls:
24.0ms
(+ x (- (tan (+ y z)) (tan a)))
18.0ms
(- (tan (+ y z)) (tan a))
7.0ms
(tan (+ y z))

series442.0ms

Counts
3 → 9
Calls
3 calls:
191.0ms
(+ x (- (tan (+ y z)) (tan a)))
179.0ms
(- (tan (+ y z)) (tan a))
72.0ms
(tan (+ y z))

simplify923.0ms

Counts
51 → 51
Iterations

Useful iterations: 3 (365.0ms)

IterNodesCost
091627
1197590
2475572
31729570
done5000570

prune176.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

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)))

rewrite178.0ms

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×prod-exp cbrt-unprod 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 → 96
Calls
4 calls:
34.0ms
(* (+ (tan y) (tan z)) (cos a))
28.0ms
(* (tan y) (tan z))
16.0ms
(* (tan y) (tan z))
93.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.1s

Counts
4 → 12
Calls
4 calls:
208.0ms
(* (+ (tan y) (tan z)) (cos a))
129.0ms
(* (tan y) (tan z))
126.0ms
(* (tan y) (tan z))
649.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify2.1s

Counts
108 → 108
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01952138
16112041
232861696
done50001631

prune521.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
39×associate-*l/
29×add-exp-log
21×add-sqr-sqrt
19×add-cbrt-cube
18×tan-quot associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt associate-*l* prod-exp
12×pow1 frac-sub
10×frac-times
9×flip3-- flip--
7×cbrt-unprod
5×flip3-+ frac-add flip-+
4×div-exp pow-prod-down *-commutative add-log-exp unswap-sqr
3×times-frac associate-*r/
2×cbrt-undiv rec-exp 1-exp associate-/r/
1×un-div-inv div-inv distribute-lft-out
Counts
4 → 114
Calls
4 calls:
33.0ms
(* (+ (tan y) (tan z)) (cos a))
16.0ms
(* (tan y) (tan z))
16.0ms
(* (tan y) (tan z))
167.0ms
(* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (/ 1 (* (- 1 (* (tan y) (tan z))) (cos a))))

series910.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (+ (tan y) (tan z)) (cos a))
101.0ms
(* (tan y) (tan z))
102.0ms
(* (tan y) (tan z))
541.0ms
(* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (/ 1 (* (- 1 (* (tan y) (tan z))) (cos a))))

simplify363.0ms

Counts
126 → 126
Iterations

Useful iterations: done (359.0ms)

IterNodesCost
02603415
18473168
done50002842

prune598.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.2b
(* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))
0.3b
(pow (* (tan y) (tan z)) 3)
0.3b
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))) (* (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (cos y) (cos z))) (+ 1 (* (* (tan y) (tan z)) (+ (* (tan y) (tan z)) 1)))))

rewrite761.0ms

Algorithm
rewrite-expression-head
Rules
120×associate-*l/
72×frac-times
58×pow1
56×add-exp-log add-cbrt-cube
45×associate-*r/
42×associate-/l/
40×frac-sub
36×tan-quot flip3-+ cos-mult flip-+
30×prod-exp cbrt-unprod
26×pow-prod-down
25×flip3-- flip--
17×associate-/r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-undiv div-exp
4×pow-sqr pow-prod-up add-log-exp
3×cube-div pow-unpow times-frac associate-/l*
2×pow-pow pow-plus associate-*r* associate-*l* pow-exp *-commutative rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down frac-2neg unpow3 div-sub cube-prod swap-sqr clear-num associate-/r* div-inv sqr-pow
Counts
4 → 190
Calls
4 calls:
70.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
117.0ms
(* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))
13.0ms
(pow (* (tan y) (tan z)) 3)
548.0ms
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))) (* (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (cos y) (cos z))) (+ 1 (* (* (tan y) (tan z)) (+ (* (tan y) (tan z)) 1)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
125.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
247.0ms
(* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))
141.0ms
(pow (* (tan y) (tan z)) 3)
2.1s
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))) (* (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (cos y) (cos z))) (+ 1 (* (* (tan y) (tan z)) (+ (* (tan y) (tan z)) 1)))))

simplify770.0ms

Counts
202 → 202
Iterations

Useful iterations: done (758.0ms)

IterNodesCost
049012959
1208610613
done50019273

prune2.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes698.0ms

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
01934
12834
done2834

end0.0ms

sample8.8s

Algorithm
intervals
Results
4.7s3903×body1280valid
2.2s2009×body640valid
609.0ms690×body320valid
525.0ms8000×pre80true
140.0ms1113×body80valid
79.0ms285×body160valid