Details

Time bar (total: 14.8s)

sample173.0ms

Algorithm
intervals
Results
102.0ms127×body1280valid
26.0ms61×body640valid
11.0ms256×pre80true
7.0ms23×body320valid
3.0ms17×body160valid
3.0ms28×body80valid

simplify76.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
099
1159
2229
3319
4379
5479
6549
7649
8829
91169
101479
done1479

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))
3.9b
(tan (+ y z))

rewrite22.0ms

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:
7.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(- (tan (+ y z)) (tan a))
3.0ms
(tan (+ y z))

series278.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(+ x (- (tan (+ y z)) (tan a)))
111.0ms
(- (tan (+ y z)) (tan a))
49.0ms
(tan (+ y z))

simplify1.3s

Counts
51 → 51
Iterations

Useful iterations: 3 (114.0ms)

IterNodesCost
091627
1197590
2434572
31054570
43933570
done5000570

prune149.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
17×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
11×add-log-exp
8×tan-quot add-exp-log add-cbrt-cube
7×distribute-lft-out
6×pow1
4×associate-/l*
3×flip3-+ associate-*r* associate-*l* associate-/r* sum-log flip-+ associate-/l/
2×+-commutative associate-+r+ frac-add associate-/r/
1×cbrt-undiv frac-times associate-+r- sub-neg flip3-- frac-2neg diff-log associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num *-commutative flip-- cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 87
Calls
4 calls:
72.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
3.0ms
(+ (tan y) (tan z))
5.0ms
(* (tan y) (tan z))

series717.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
207.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
91.0ms
(+ (tan y) (tan z))
91.0ms
(* (tan y) (tan z))

simplify1.2s

Counts
99 → 99
Iterations

Useful iterations: 3 (372.0ms)

IterNodesCost
01731733
14201668
211841568
334971567
done50011567

prune334.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

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-exp-log add-cbrt-cube
7×sum-log
6×pow1
4×flip3-+ frac-add flip-+ associate-/l*
3×associate-*r* associate-*l* associate-/r* associate-/l/
2×+-commutative distribute-rgt-neg-in neg-log associate-/r/ distribute-neg-frac
1×cbrt-undiv neg-sub0 frac-times associate-+r- associate-+l+ flip3-- frac-2neg associate-*r/ div-exp unsub-neg pow-prod-down associate-*l/ prod-exp clear-num *-commutative flip-- cbrt-unprod div-inv unswap-sqr
Counts
4 → 94
Calls
4 calls:
106.0ms
(+ (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (- (tan a)))
11.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
3.0ms
(+ (tan y) (tan z))
5.0ms
(* (tan y) (tan z))

series691.0ms

Counts
4 → 12
Calls
4 calls:
316.0ms
(+ (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (- (tan a)))
200.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
88.0ms
(+ (tan y) (tan z))
89.0ms
(* (tan y) (tan z))

simplify539.0ms

Counts
106 → 106
Iterations

Useful iterations: done (534.0ms)

IterNodesCost
01982022
15151888
216641810
done50021779

prune332.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.3b
(* (tan a) (tan a))
0.4b
(/ (- (* (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (* (tan a) (tan a))) (+ (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a)))
0.4b
(* (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
42×tan-quot
31×add-sqr-sqrt
26×frac-times flip3-+ flip-+ associate-/l/
25×add-cube-cbrt
24×frac-sub
21×distribute-lft-out
20×pow1 times-frac
18×associate-*r/ associate-*l/
12×add-exp-log add-cbrt-cube
10×associate-*r* associate-*l*
9×swap-sqr
6×difference-of-squares
5×associate-/r*
4×associate-/r/ associate-/l* add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×pow2 pow-plus frac-add pow-sqr pow-prod-up
1×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub div-exp clear-num flip-- div-inv
Counts
4 → 161
Calls
4 calls:
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan a) (tan a))
214.0ms
(/ (- (* (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (* (tan a) (tan a))) (+ (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a)))
115.0ms
(* (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (tan y) (tan z))
35.0ms
(* (tan a) (tan a))
1.2s
(/ (- (* (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (* (tan a) (tan a))) (+ (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a)))
356.0ms
(* (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))

simplify952.0ms

Counts
173 → 173
Iterations

Useful iterations: 2 (258.0ms)

IterNodesCost
03048279
18467473
235727078
done50017078

prune607.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes394.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02347
13147
done3147

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.8s3884×body1280valid
872.0ms2024×body640valid
308.0ms8000×pre80true
185.0ms629×body320valid
101.0ms1169×body80valid
66.0ms294×body160valid