Details

Time bar (total: 38.8s)

sample457.0ms

Algorithm
intervals
Results
262.0ms125×body1280valid
108.0ms62×body640valid
28.0ms256×pre80true
16.0ms22×body320valid
11.0ms42×body80valid
3.0ms5×body160valid

simplify75.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
75.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize32.0ms

Local error

Found 3 expressions with local error:

3.4b
(tan (+ y z))
0.2b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))

rewrite32.0ms

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 insert-posit16
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 → 45
Calls
3 calls:
Slowest
13.0ms
(- (tan (+ y z)) (tan a))
10.0ms
(+ x (- (tan (+ y z)) (tan a)))
8.0ms
(tan (+ y z))

series402.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
190.0ms
(+ x (- (tan (+ y z)) (tan a)))
133.0ms
(- (tan (+ y z)) (tan a))
78.0ms
(tan (+ y z))

simplify1.7s

Counts
25 → 54
Calls
25 calls:
Slowest
512.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
182.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
126.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
121.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
107.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))

prune575.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite193.0ms

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
4×insert-posit16
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 → 71
Calls
4 calls:
Slowest
99.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
49.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
32.0ms
(* (tan y) (tan z))
13.0ms
(+ (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
619.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
504.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
123.0ms
(* (tan y) (tan z))
117.0ms
(+ (tan y) (tan z))

simplify3.9s

Counts
45 → 83
Calls
45 calls:
Slowest
441.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
359.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
338.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
337.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))) (/ (sin a) (cos a)))
332.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

2.7b
(log (exp (+ (tan y) (tan z))))
0.4b
(exp (+ (tan y) (tan z)))
0.2b
(* (tan y) (tan z))
0.2b
(+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
12×add-log-exp
11×add-sqr-sqrt
9×add-cube-cbrt
8×exp-prod
7×pow1
6×add-cbrt-cube add-exp-log
5×log-pow
4×log-prod tan-quot insert-posit16 distribute-lft-out
3×sum-log associate-*r* associate-*l*
2×associate-+r+ exp-sum rem-exp-log
1×frac-times +-commutative associate-+r- sub-neg flip3-+ diff-log rem-log-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ distribute-lft-out-- unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
214.0ms
(+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a)))
20.0ms
(* (tan y) (tan z))
20.0ms
(exp (+ (tan y) (tan z)))
17.0ms
(log (exp (+ (tan y) (tan z))))

series941.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
532.0ms
(+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a)))
144.0ms
(* (tan y) (tan z))
140.0ms
(exp (+ (tan y) (tan z)))
125.0ms
(log (exp (+ (tan y) (tan z))))

simplify2.6s

Counts
49 → 85
Calls
49 calls:
Slowest
339.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
337.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
327.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
268.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))
204.0ms
(* (exp x) (exp (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a))))

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

2.7b
(log (exp (+ (tan y) (tan z))))
2.3b
(exp (+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a))))
0.4b
(exp (+ (tan y) (tan z)))
0.2b
(* (tan y) (tan z))

rewrite855.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
13×exp-prod add-log-exp
12×add-sqr-sqrt
10×add-cube-cbrt
7×pow1
6×add-cbrt-cube add-exp-log
5×log-pow rem-exp-log
4×log-prod tan-quot insert-posit16 distribute-lft-out
3×sum-log associate-*r* associate-*l* exp-sum
1×frac-times associate-+r- exp-diff diff-log rem-log-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
780.0ms
(exp (+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a))))
31.0ms
(exp (+ (tan y) (tan z)))
26.0ms
(* (tan y) (tan z))
17.0ms
(log (exp (+ (tan y) (tan z))))

series945.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
568.0ms
(exp (+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a))))
131.0ms
(exp (+ (tan y) (tan z)))
125.0ms
(* (tan y) (tan z))
120.0ms
(log (exp (+ (tan y) (tan z))))

simplify2.7s

Counts
52 → 85
Calls
52 calls:
Slowest
451.0ms
(exp (- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a))))
410.0ms
(exp (- (+ x (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))))) (/ (sin a) (cos a))))
357.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
255.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))
243.0ms
(exp (* (cbrt (+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a)))) (cbrt (+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a))))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes541.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample16.2s

Algorithm
intervals
Results
10.6s3875×body1280valid
2.9s1980×body640valid
1.0s8000×pre80true
764.0ms674×body320valid
317.0ms1186×body80valid
205.0ms285×body160valid