Details

Time bar (total: 1.2m)

sample406.0ms

Algorithm
intervals
Results
226.0ms98×body1280valid
46.0ms70×body80valid
43.0ms51×body640valid
21.0ms29×body320valid
3.0ms8×body160valid

simplify198.0ms

Calls
1 calls:
Slowest
146.0ms
(* r (/ (sin b) (cos (+ a b))))

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize26.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (+ a b))
0.3b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
19×times-frac
13×associate-*r*
10×add-cbrt-cube add-exp-log
9×associate-*r/
7×associate-/l*
6×associate-/r*
5×pow1
3×clear-num associate-*l* insert-posit16 add-log-exp
2×cbrt-undiv cos-sum frac-2neg div-exp prod-exp un-div-inv cbrt-unprod div-inv unswap-sqr
1×+-commutative pow-prod-down *-commutative
Calls
3 calls:
Slowest
65.0ms
(cos (+ a b))
64.0ms
(* r (/ (sin b) (cos (+ a b))))
14.0ms
(/ (sin b) (cos (+ a b)))

series302.0ms

Calls
3 calls:
Slowest
137.0ms
(* r (/ (sin b) (cos (+ a b))))
83.0ms
(/ (sin b) (cos (+ a b)))
82.0ms
(cos (+ a b))

simplify2.6s

Calls
71 calls:
Slowest
592.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
315.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
248.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
213.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
142.0ms
(* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b)))))

prune904.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin b) (sin a))
0.2b
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
0.2b
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
0.1b
(- (* (cos b) (cos a)) (* (sin b) (sin a)))

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
155×add-sqr-sqrt
113×*-un-lft-identity
67×times-frac
44×associate-*r*
42×associate-*l*
40×add-cube-cbrt
39×unswap-sqr
36×distribute-lft-out-- difference-of-squares
22×associate-/r*
17×associate-*r/
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult associate-/l*
6×cos-mult add-log-exp
4×insert-posit16
3×clear-num flip3-- prod-exp frac-sub cbrt-unprod flip-- sub-div
2×cbrt-undiv frac-2neg div-exp pow-prod-down un-div-inv *-commutative div-inv
1×sub-neg diff-log
Calls
4 calls:
Slowest
288.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
95.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
84.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
31.0ms
(* (sin b) (sin a))

series677.0ms

Calls
4 calls:
Slowest
294.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
171.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
130.0ms
(- (* (cos b) (cos a)) (* (sin b) (sin a)))
81.0ms
(* (sin b) (sin a))

simplify9.1s

Calls
193 calls:
Slowest
384.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos b) (cos a)) (* (sin b) (sin a))) (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
364.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
328.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))
325.0ms
(- (+ (cos (+ b a)) (cos (- b a))) (- (cos (- b a)) (cos (+ b a))))
273.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos b) (cos a)) (* (sin b) (sin a)))))

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

4.0b
(log (exp (* (sin b) (sin a))))
0.2b
(* (sin b) (sin a))
0.2b
(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a))))))
0.2b
(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a)))))))

rewrite575.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt *-un-lft-identity
55×times-frac
40×add-cube-cbrt
39×associate-*r*
32×distribute-lft-out--
30×log-pow
25×pow1 associate-*l*
18×associate-/r*
16×difference-of-squares
15×associate-*r/
14×add-exp-log
13×add-cbrt-cube
12×exp-prod unswap-sqr
7×associate-/l*
5×add-log-exp
4×associate-/r/ insert-posit16
3×log-prod clear-num prod-exp *-commutative cbrt-unprod
2×cbrt-undiv frac-2neg flip3-- div-exp rem-log-exp pow-prod-down un-div-inv div-inv flip--
1×exp-to-pow sin-mult
Calls
4 calls:
Slowest
392.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a)))))))
128.0ms
(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a))))))
29.0ms
(log (exp (* (sin b) (sin a))))
22.0ms
(* (sin b) (sin a))

series583.0ms

Calls
4 calls:
Slowest
274.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a)))))))
152.0ms
(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a))))))
88.0ms
(* (sin b) (sin a))
69.0ms
(log (exp (* (sin b) (sin a))))

simplify27.1s

Calls
171 calls:
Slowest
508.0ms
(/ (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a))))) (sin b))
473.0ms
(/ (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a))))) (sin b))
432.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a))))) (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a)))))) (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a)))))))
428.0ms
(/ (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a))))) (sin b))
428.0ms
(/ (- (* (cos b) (cos a)) (log (exp (* (sin b) (sin a))))) (sin b))

prune2.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

4.4b
(log (exp (sin a)))
0.2b
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a))))))
0.2b
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a)))))))
0.1b
(* (sin b) (log (exp (sin a))))

rewrite591.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
110×*-un-lft-identity
67×times-frac
46×associate-*r*
45×add-cube-cbrt
38×associate-*l*
35×unswap-sqr
32×distribute-lft-out-- difference-of-squares
22×associate-/r*
17×associate-*r/
14×add-exp-log
13×add-cbrt-cube
10×pow1
9×log-prod
8×log-pow
7×associate-/l*
6×exp-prod
4×associate-/r/ insert-posit16 add-log-exp
3×distribute-rgt-in clear-num distribute-lft-in prod-exp cbrt-unprod
2×cbrt-undiv frac-2neg flip3-- div-exp rem-log-exp pow-prod-down un-div-inv *-commutative div-inv flip--
Calls
4 calls:
Slowest
399.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a)))))))
145.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a))))))
27.0ms
(* (sin b) (log (exp (sin a))))
16.0ms
(log (exp (sin a)))

series465.0ms

Calls
4 calls:
Slowest
263.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a)))))))
135.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a))))))
59.0ms
(* (sin b) (log (exp (sin a))))
8.0ms
(log (exp (sin a)))

simplify9.5s

Calls
191 calls:
Slowest
683.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (log (exp (sin a)))) (* (sin b) (log (exp (sin a))))) (* (* (cos b) (cos a)) (* (sin b) (log (exp (sin a)))))))
381.0ms
(- (+ (* 1/120 (pow a 5)) a) (* 1/6 (pow a 3)))
380.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a))))) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a)))))) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a)))))))
377.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a)))))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a))))))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (log (exp (sin a))))))))
334.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin b) (log (exp (sin a)))) (* (sin b) (log (exp (sin a))))) (* (* (cos b) (cos a)) (* (sin b) (log (exp (sin a)))))))

prune3.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes410.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch4.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
4.2s3020×body1280valid
1.5s1778×body640valid
859.0ms792×body320valid
349.0ms2079×body80valid
119.0ms332×body160valid