Details

Time bar (total: 25.1s)

sample232.0ms

Algorithm
intervals
Results
144.0ms127×body1280valid
34.0ms62×body640valid
12.0ms256×pre80true
9.0ms25×body320valid
4.0ms13×body160valid
3.0ms29×body80valid

simplify88.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize60.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.2b
(- (tan (+ y z)) (tan a))
4.5b
(tan (+ y z))

rewrite59.0ms

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:
19.0ms
(+ x (- (tan (+ y z)) (tan a)))
28.0ms
(- (tan (+ y z)) (tan a))
10.0ms
(tan (+ y z))

series392.0ms

Counts
3 → 9
Calls
3 calls:
176.0ms
(+ x (- (tan (+ y z)) (tan a)))
146.0ms
(- (tan (+ y z)) (tan a))
71.0ms
(tan (+ y z))

simplify584.0ms

Counts
51 → 51

prune223.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

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

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×tan-quot
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
12×frac-sub
10×add-cube-cbrt *-un-lft-identity
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×cbrt-undiv frac-times associate-*r/ div-exp pow-prod-down associate-/r/ *-commutative unswap-sqr
1×sub-neg frac-2neg diff-log div-sub clear-num associate-/r* div-inv
Counts
4 → 92
Calls
4 calls:
39.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
81.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
25.0ms
(* (tan y) (tan z))
28.0ms
(* (tan y) (tan z))

series1.5s

Counts
4 → 12
Calls
4 calls:
437.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
751.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
135.0ms
(* (tan y) (tan z))
156.0ms
(* (tan y) (tan z))

simplify1.4s

Counts
104 → 104

prune725.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
64×associate-*l/
60×times-frac
41×associate-/r/
38×add-sqr-sqrt
34×add-exp-log add-cube-cbrt *-un-lft-identity
30×frac-sub
28×tan-quot
22×add-cbrt-cube
21×flip3-- flip--
18×associate-/r*
14×div-exp
10×flip3-+ frac-add flip-+
9×pow1
7×cbrt-undiv
6×associate-*r* associate-*l* prod-exp div-inv
4×cbrt-unprod associate-/l* add-log-exp
3×rec-exp 1-exp
2×frac-times frac-2neg associate-*r/ pow-prod-down clear-num *-commutative associate-/l/ unswap-sqr
1×pow-flip inv-pow
Counts
4 → 161
Calls
4 calls:
36.0ms
(* (tan y) (tan z))
30.0ms
(* (tan y) (tan z))
136.0ms
(/ 1 (/ (* (- 1 (* (tan y) (tan z))) (cos a)) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))))
117.0ms
(/ (* (- 1 (* (tan y) (tan z))) (cos a)) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))

series1.7s

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (tan y) (tan z))
123.0ms
(* (tan y) (tan z))
680.0ms
(/ 1 (/ (* (- 1 (* (tan y) (tan z))) (cos a)) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))))
801.0ms
(/ (* (- 1 (* (tan y) (tan z))) (cos a)) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))

simplify1.7s

Counts
173 → 173

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
126×add-exp-log
99×add-cbrt-cube
59×prod-exp
57×pow1
44×cbrt-unprod
39×div-exp
36×tan-quot
27×cbrt-undiv
26×pow-prod-down
22×frac-times associate-*l/
16×associate-*r/
10×add-sqr-sqrt
9×times-frac associate-/r/
8×add-cube-cbrt *-un-lft-identity
7×associate-/l*
6×1-exp cos-mult
5×associate-*r* associate-*l*
4×flip3-- pow-sqr pow-prod-up flip-- add-log-exp
3×*-commutative div-inv
2×flip3-+ pow-plus flip-+
1×pow2 frac-2neg swap-sqr clear-num associate-/r* associate-/l/ unswap-sqr
Counts
4 → 164
Calls
4 calls:
18.0ms
(* (tan y) (tan z))
91.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
71.0ms
(* (* (cos y) (cos z)) (* (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
106.0ms
(/ (/ (* 1 (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a))))) (* (- 1 (* (tan y) (tan z))) (cos a))) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z)))))

series2.2s

Counts
4 → 12
Calls
4 calls:
121.0ms
(* (tan y) (tan z))
158.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
266.0ms
(* (* (cos y) (cos z)) (* (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
1.6s
(/ (/ (* 1 (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a))))) (* (- 1 (* (tan y) (tan z))) (cos a))) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z)))))

simplify623.0ms

Counts
176 → 176

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes499.0ms

Accuracy

-1.1% (0.1b remaining)

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

bsearch0.0ms

simplify891.0ms

end0.0ms

sample9.1s

Algorithm
intervals
Results
4.6s3835×body1280valid
2.5s2042×body640valid
918.0ms8000×pre80true
396.0ms692×body320valid
142.0ms1143×body80valid
78.0ms288×body160valid