Details

Time bar (total: 1.2m)

sample571.0ms

Algorithm
intervals
Results
252.0ms122×body1280valid
118.0ms73×body640valid
58.0ms18×body320valid
55.0ms35×body80valid
36.0ms256×pre80true
7.0ms8×body160valid

simplify80.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
80.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize39.0ms

Local error

Found 3 expressions with local error:

2.8b
(tan (+ y z))
0.1b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite41.0ms

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
22.0ms
(- (tan (+ y z)) (tan a))
13.0ms
(+ x (- (tan (+ y z)) (tan a)))
6.0ms
(tan (+ y z))

series501.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
230.0ms
(+ x (- (tan (+ y z)) (tan a)))
186.0ms
(- (tan (+ y z)) (tan a))
84.0ms
(tan (+ y z))

simplify4.2s

Counts
62 → 54
Calls
62 calls:
Slowest
450.0ms
(- (* x x) (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))))
432.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
377.0ms
(* (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))) (- (tan (+ y z)) (tan a)))
233.0ms
(- (pow (tan (+ y z)) 3) (pow (tan a) 3))
187.0ms
(+ (* x x) (- (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))) (* x (- (tan (+ y z)) (tan a)))))

prune631.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b
(+ (tan y) (tan z))

rewrite202.0ms

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
113.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
64.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms
(* (tan y) (tan z))
8.0ms
(+ (tan y) (tan z))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
671.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
549.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
147.0ms
(* (tan y) (tan z))
126.0ms
(+ (tan y) (tan z))

simplify9.2s

Counts
92 → 83
Calls
92 calls:
Slowest
700.0ms
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
557.0ms
(+ (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ (* (tan a) (tan a)) (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
493.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
436.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
328.0ms
(- (pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3) (pow (tan a) 3))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

3.5b
(log (exp (* (tan y) (tan z))))
0.3b
(* (tan y) (tan z))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
0.1b
(exp (* (tan y) (tan z)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×*-un-lft-identity add-log-exp
7×pow1 add-cube-cbrt
6×add-cbrt-cube add-exp-log
5×tan-quot
4×insert-posit16
3×log-prod associate-*r* associate-*l* log-pow
2×exp-prod exp-to-pow difference-of-squares
1×frac-times sub-neg times-frac flip3-- diff-log rem-log-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-- distribute-lft-out-- unswap-sqr rem-exp-log
Counts
4 → 65
Calls
4 calls:
Slowest
110.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
22.0ms
(* (tan y) (tan z))
21.0ms
(exp (* (tan y) (tan z)))
5.0ms
(log (exp (* (tan y) (tan z))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
651.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
198.0ms
(exp (* (tan y) (tan z)))
165.0ms
(log (exp (* (tan y) (tan z))))
145.0ms
(* (tan y) (tan z))

simplify9.1s

Counts
83 → 77
Calls
83 calls:
Slowest
538.0ms
(* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z)))
361.0ms
(* (- 1 (log (exp (* (tan y) (tan z))))) (cos a))
332.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
259.0ms
(+ (* 1/3 (* z (pow y 3))) (+ (* z y) 1))
255.0ms
(- (* (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z))))))) (* (tan a) (tan a)))

prune981.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

27.5b
(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))
3.5b
(log (exp (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))))
0.3b
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
0.3b
(* (tan z) (tan y))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
228×tan-quot
147×frac-times
87×associate-*l/
75×associate-*r/
63×cbrt-div
46×pow1
18×add-cbrt-cube pow-prod-down add-exp-log
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
5×log-pow
4×exp-prod associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 add-log-exp
3×log-prod
2×cbrt-prod pow-plus *-commutative
1×pow2 pow1/3 swap-sqr rem-log-exp pow3 rem-cbrt-cube unswap-sqr
Counts
4 → 163
Calls
4 calls:
Slowest
148.0ms
(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))
68.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
15.0ms
(* (tan z) (tan y))
2.0ms
(log (exp (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))))

series483.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
126.0ms
(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))
112.0ms
(log (exp (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))))
110.0ms
(* (tan z) (tan y))

simplify27.6s

Counts
248 → 175
Calls
248 calls:
Slowest
638.0ms
(* (* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y))) (* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y))))
537.0ms
(* (* (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y)))) (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y)))))
523.0ms
(* (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))) (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))
347.0ms
(log (exp (* (cbrt (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cbrt (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))))))
346.0ms
(cbrt (* (* (* (tan z) (sin y)) (* (tan z) (tan y))) (* (sin z) (sin y))))

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes361.0ms

Accuracy

0% (0.2b remaining)

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

bsearch7.0ms

end0.0ms

sample12.1s

Algorithm
intervals
Results
7.4s3939×body1280valid
2.9s2001×body640valid
726.0ms8000×pre80true
410.0ms652×body320valid
241.0ms1129×body80valid
166.0ms279×body160valid