Details

Time bar (total: 41.1s)

sample1.7s

Algorithm
intervals
Results
1.4s217×body10240exit
110.0ms268×body80valid
6.0ms11×body160valid

simplify333.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
332.0ms
(- (* PI l) (* (/ 1 (* F F)) (tan (* PI l))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.6b

localize33.0ms

Local error

Found 4 expressions with local error:

7.1b
(/ (tan (* PI l)) (* F F))
4.3b
(tan (* PI l))
0.3b
(* PI l)
0.3b
(* PI l)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×times-frac prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv div-exp pow-prod-down tan-quot *-commutative unswap-sqr
1×clear-num associate-/r* frac-2neg div-inv associate-/l/
Counts
4 → 78
Calls
4 calls:
Slowest
42.0ms
(/ (tan (* PI l)) (* F F))
9.0ms
(tan (* PI l))
6.0ms
(* PI l)
5.0ms
(* PI l)

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ (tan (* PI l)) (* F F))
95.0ms
(tan (* PI l))
41.0ms
(* PI l)
39.0ms
(* PI l)

simplify2.4s

Counts
43 → 90
Calls
43 calls:
Slowest
453.0ms
(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) (* F F)) (* F F)))
412.0ms
(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) F) (* (* F F) F)))
359.0ms
(+ (/ (* PI l) (pow F 2)) (+ (* 2/15 (/ (* (pow PI 5) (pow l 5)) (pow F 2))) (* 1/3 (/ (* (pow PI 3) (pow l 3)) (pow F 2)))))
305.0ms
(* (* (* PI PI) PI) (* (* l l) l))
299.0ms
(* (* (* PI PI) PI) (* (* l l) l))

prune882.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.6b

localize31.0ms

Local error

Found 4 expressions with local error:

4.3b
(tan (* PI l))
0.3b
(* PI l)
0.3b
(* PI l)
0.2b
(/ (tan (* PI l)) F)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
10×add-cbrt-cube add-exp-log
9×times-frac
8×pow1
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×pow-prod-down prod-exp tan-quot *-commutative cbrt-unprod unswap-sqr
1×cbrt-undiv clear-num frac-2neg div-exp div-inv associate-/l/
Counts
4 → 84
Calls
4 calls:
Slowest
23.0ms
(/ (tan (* PI l)) F)
17.0ms
(tan (* PI l))
11.0ms
(* PI l)
11.0ms
(* PI l)

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ (tan (* PI l)) F)
84.0ms
(tan (* PI l))
40.0ms
(* PI l)
37.0ms
(* PI l)

simplify1.9s

Counts
55 → 96
Calls
55 calls:
Slowest
425.0ms
(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* F F) F))
330.0ms
(* (* (* PI PI) PI) (* (* l l) l))
295.0ms
(* (* (* PI PI) PI) (* (* l l) l))
208.0ms
(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
188.0ms
(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))

prune985.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

4.3b
(tan (* PI l))
0.9b
(/ 1 (/ F (tan (* PI l))))
0.3b
(* PI l)
0.3b
(* PI l)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
55×add-sqr-sqrt
51×*-un-lft-identity add-cube-cbrt
19×add-exp-log
14×associate-/r*
13×add-cbrt-cube
9×pow1
7×div-exp
6×associate-*r* associate-*l*
5×tan-quot associate-/r/ div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/l*
2×rec-exp 1-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×clear-num frac-2neg pow-flip inv-pow
Counts
4 → 136
Calls
4 calls:
Slowest
14.0ms
(/ 1 (/ F (tan (* PI l))))
10.0ms
(* PI l)
10.0ms
(tan (* PI l))
8.0ms
(* PI l)

series342.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(/ 1 (/ F (tan (* PI l))))
117.0ms
(tan (* PI l))
38.0ms
(* PI l)
29.0ms
(* PI l)

simplify7.0s

Counts
138 → 148
Calls
138 calls:
Slowest
526.0ms
(/ (* (* 1 1) 1) (* (* (/ F (tan (* PI l))) (/ F (tan (* PI l)))) (/ F (tan (* PI l)))))
383.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt F) (cbrt F)) (* (cbrt (tan (* PI l))) (cbrt (tan (* PI l))))))
333.0ms
(* (* (* PI PI) PI) (* (* l l) l))
264.0ms
(* (* (* PI PI) PI) (* (* l l) l))
263.0ms
(/ (sqrt 1) (/ (* (cbrt F) (cbrt F)) (* (cbrt (tan (* PI l))) (cbrt (tan (* PI l))))))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

Local error

Found 4 expressions with local error:

4.3b
(tan (* PI l))
4.3b
(tan (* PI l))
4.3b
(tan (* PI l))
0.6b
(cbrt (tan (* PI l)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube tan-quot add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
1×cbrt-div pow1/3
Counts
4 → 48
Calls
4 calls:
Slowest
17.0ms
(tan (* PI l))
13.0ms
(tan (* PI l))
11.0ms
(tan (* PI l))
10.0ms
(cbrt (tan (* PI l)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
296.0ms
(cbrt (tan (* PI l)))
103.0ms
(tan (* PI l))
86.0ms
(tan (* PI l))
67.0ms
(tan (* PI l))

simplify1.3s

Counts
16 → 60
Calls
16 calls:
Slowest
260.0ms
(pow (/ (sin (* PI l)) (cos (* PI l))) 1/3)
226.0ms
(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
222.0ms
(pow (/ (sin (* PI l)) (cos (* PI l))) 1/3)
194.0ms
(+ (* 1/9 (* (exp (* 1/3 (+ (log l) (log PI)))) (* (pow PI 2) (pow l 2)))) (+ (* 13/405 (* (exp (* 1/3 (+ (log l) (log PI)))) (* (pow PI 4) (pow l 4)))) (exp (* 1/3 (+ (log l) (log PI))))))
186.0ms
(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))

prune769.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.5b

regimes459.0ms

Accuracy

0% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 1.1b

bsearch2.0ms

end0.0ms

sample19.9s

Algorithm
intervals
Results
16.6s7462×body10240exit
2.9s8841×body80valid
128.0ms266×body160valid