Details

Time bar (total: 30.8s)

sample346.0ms

Algorithm
intervals
Results
179.0ms124×body1280valid
53.0ms256×pre80true
44.0ms58×body640valid
16.0ms27×body320valid
6.0ms35×body80valid
4.0ms12×body160valid

simplify6.1s

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b
(- (tan (+ y z)) (tan a))
0.2b
(+ x (- (tan (+ y z)) (tan a)))
3.5b
(tan (+ y z))

rewrite67.0ms

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:
32.0ms
(- (tan (+ y z)) (tan a))
23.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(tan (+ y z))

series468.0ms

Counts
3 → 9
Calls
3 calls:
182.0ms
(- (tan (+ y z)) (tan a))
191.0ms
(+ x (- (tan (+ y z)) (tan a)))
95.0ms
(tan (+ y z))

simplify782.0ms

Counts
51 → 51
Iterations
IterNodes
done5000
31731
2474
1197
091

prune333.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
0.2b
(+ (tan y) (tan z))
0.2b
(* (tan z) (tan y))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt add-log-exp
7×tan-quot
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
3×sum-log associate-*r* associate-*l* distribute-lft-out
2×+-commutative associate-+r+ sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- times-frac flip3-- pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-- unswap-sqr
Counts
4 → 67
Calls
4 calls:
94.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
172.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
6.0ms
(+ (tan y) (tan z))
12.0ms
(* (tan z) (tan y))

series1.5s

Counts
4 → 12
Calls
4 calls:
611.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
569.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
154.0ms
(+ (tan y) (tan z))
137.0ms
(* (tan z) (tan y))

simplify743.0ms

Counts
79 → 79
Iterations
IterNodes
done5000
21220
1379
0156

prune664.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin y) (cos z))
0.2b
(/ (sin y) (* (cos y) (- 1 (* (/ (sin y) (cos z)) (/ (sin z) (cos y))))))
0.2b
(* (/ (sin y) (cos z)) (/ (sin z) (cos y)))
0.2b
(* (/ (sin y) (cos z)) (/ (sin z) (cos y)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
56×times-frac
42×*-un-lft-identity add-cube-cbrt
35×add-cbrt-cube add-exp-log
26×associate-*r* associate-*l*
11×cbrt-undiv div-exp
9×prod-exp cbrt-unprod
8×pow1 unswap-sqr
6×div-inv associate-/l*
4×associate-/r* associate-*r/ add-log-exp
2×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-/r/ *-commutative
1×flip3-- flip--
Counts
4 → 150
Calls
4 calls:
15.0ms
(/ (sin y) (cos z))
27.0ms
(/ (sin y) (* (cos y) (- 1 (* (/ (sin y) (cos z)) (/ (sin z) (cos y))))))
53.0ms
(* (/ (sin y) (cos z)) (/ (sin z) (cos y)))
32.0ms
(* (/ (sin y) (cos z)) (/ (sin z) (cos y)))

series565.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ (sin y) (cos z))
211.0ms
(/ (sin y) (* (cos y) (- 1 (* (/ (sin y) (cos z)) (/ (sin z) (cos y))))))
139.0ms
(* (/ (sin y) (cos z)) (/ (sin z) (cos y)))
151.0ms
(* (/ (sin y) (cos z)) (/ (sin z) (cos y)))

simplify1.7s

Counts
162 → 162
Iterations
IterNodes
done5001
23359
1581
0203

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.1b
(+ (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) x) (- (tan a)))
0.2b
(+ (tan y) (tan z))
0.2b
(* (tan y) (tan z))

rewrite383.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
17×add-sqr-sqrt
16×add-log-exp
15×add-cube-cbrt
12×times-frac
11×distribute-lft-out
10×tan-quot
8×add-cbrt-cube add-exp-log
7×sum-log
6×pow1
4×flip3-+ frac-add flip-+ associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×+-commutative distribute-rgt-neg-in neg-log associate-/r/ distribute-neg-frac
1×neg-sub0 frac-times cbrt-undiv associate-+l+ clear-num associate-+r- frac-2neg flip3-- div-exp unsub-neg pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod div-inv flip-- unswap-sqr
Counts
4 → 94
Calls
4 calls:
44.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
288.0ms
(+ (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) x) (- (tan a)))
13.0ms
(+ (tan y) (tan z))
33.0ms
(* (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
301.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
832.0ms
(+ (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) x) (- (tan a)))
148.0ms
(+ (tan y) (tan z))
123.0ms
(* (tan y) (tan z))

simplify960.0ms

Counts
106 → 106
Iterations
IterNodes
done5001
22232
1514
0198

prune839.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes737.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done28
128
023

end0.0ms

sample10.9s

Algorithm
intervals
Results
6.5s3837×body1280valid
2.4s2048×body640valid
546.0ms8000×pre80true
531.0ms717×body320valid
247.0ms1107×body80valid
168.0ms291×body160valid