Details

Time bar (total: 31.7s)

sample672.0ms

Algorithm
intervals
Results
242.0ms66×body640valid
124.0ms88×body1280valid
47.0ms66×body80valid
25.0ms27×body320valid
4.0ms9×body160valid

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
56.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize46.0ms

Local error

Found 3 expressions with local error:

3.5b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
3×associate-/r* times-frac associate-*r* associate-*l* insert-posit16 add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum clear-num frac-2neg pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 50
Calls
3 calls:
Slowest
36.0ms
(cos (+ a b))
12.0ms
(/ (* r (sin b)) (cos (+ a b)))
8.0ms
(* r (sin b))

series260.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
168.0ms
(/ (* r (sin b)) (cos (+ a b)))
61.0ms
(* r (sin b))
31.0ms
(cos (+ a b))

simplify1.4s

Counts
33 → 59
Calls
33 calls:
Slowest
334.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
210.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
209.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
176.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
128.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune678.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* (sin a) (sin b))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b
(* (cos a) (cos b))

rewrite117.0ms

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* add-log-exp
5×cos-mult sin-mult
4×associate-/r/ insert-posit16
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×clear-num sub-neg frac-2neg diff-log div-inv associate-/l*
Counts
4 → 81
Calls
4 calls:
Slowest
37.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
37.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
22.0ms
(* (sin a) (sin b))
18.0ms
(* (cos a) (cos b))

series551.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
324.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
118.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms
(* (sin a) (sin b))
43.0ms
(* (cos a) (cos b))

simplify4.3s

Counts
54 → 93
Calls
54 calls:
Slowest
816.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
363.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
362.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
355.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
283.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×associate-*r*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×insert-posit16
3×associate-/r* flip3-- prod-exp frac-sub cbrt-unprod flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num sub-neg frac-2neg diff-log associate-*r/
Counts
4 → 104
Calls
4 calls:
Slowest
103.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms
(* (sin a) (sin b))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

series677.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
330.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
181.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
103.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
63.0ms
(* (sin a) (sin b))

simplify5.6s

Counts
83 → 116
Calls
83 calls:
Slowest
410.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
387.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
375.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
297.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
292.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity times-frac add-cube-cbrt
13×add-cbrt-cube associate-*l* add-exp-log
6×pow1 associate-/r* associate-/l* add-log-exp
4×insert-posit16
3×cbrt-undiv div-exp associate-*r* div-inv
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×sub-neg diff-log pow-prod-down associate-*l/ *-commutative
Counts
4 → 104
Calls
4 calls:
Slowest
39.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
23.0ms
(* (/ (cos b) (sin b)) (cos a))
15.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
12.0ms
(/ (cos b) (sin b))

series552.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
270.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
133.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
107.0ms
(* (/ (cos b) (sin b)) (cos a))
41.0ms
(/ (cos b) (sin b))

simplify4.3s

Counts
90 → 116
Calls
90 calls:
Slowest
441.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
338.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
329.0ms
(/ (* (* r r) r) (* (* (- (* (/ (cos b) (sin b)) (cos a)) (sin a)) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))) (- (* (/ (cos b) (sin b)) (cos a)) (sin a))))
311.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))
293.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.1s2964×body1280valid
1.7s1793×body640valid
744.0ms2112×body80valid
416.0ms777×body320valid
176.0ms355×body160valid