Details

Time bar (total: 32.2s)

sample335.0ms

Algorithm
intervals
Results
93.0ms64×body640valid
92.0ms88×body1280valid
14.0ms72×body80valid
10.0ms22×body320valid
3.0ms10×body160valid

simplify54.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
53.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize36.0ms

Local error

Found 3 expressions with local error:

4.4b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.2b
(* r (sin b))

rewrite72.0ms

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
(/ (* r (sin b)) (cos (+ a b)))
16.0ms
(cos (+ a b))
16.0ms
(* r (sin b))

series228.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
148.0ms
(/ (* r (sin b)) (cos (+ a b)))
53.0ms
(* r (sin b))
26.0ms
(cos (+ a b))

simplify1.4s

Counts
33 → 59
Calls
33 calls:
Slowest
299.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
216.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
201.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
174.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
143.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune653.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

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

rewrite97.0ms

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×sin-mult
4×associate-/r/ cos-mult 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 → 80
Calls
4 calls:
Slowest
35.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
32.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
15.0ms
(* r (sin b))
14.0ms
(* (sin a) (sin b))

series549.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
125.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
61.0ms
(* r (sin b))
55.0ms
(* (sin a) (sin b))

simplify3.8s

Counts
53 → 92
Calls
53 calls:
Slowest
366.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
355.0ms
(/ (* (* (* 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)))))
328.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (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)))))
323.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
321.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))
0.2b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* r (sin b))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
27×add-sqr-sqrt
23×*-un-lft-identity associate-*r* add-cube-cbrt
22×add-cbrt-cube
18×times-frac
14×pow1 prod-exp
8×associate-/r/ cbrt-unprod
7×associate-*l*
6×div-exp
5×pow-prod-down sin-mult
4×cos-mult insert-posit16 add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp *-commutative associate-/l*
2×flip3-- frac-sub div-inv flip-- sub-div unswap-sqr
1×clear-num frac-2neg associate-*r/ un-div-inv pow-flip inv-pow
Counts
4 → 118
Calls
4 calls:
Slowest
106.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
38.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
15.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series552.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
296.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
142.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
67.0ms
(* (sin a) (sin b))
46.0ms
(* r (sin b))

simplify7.0s

Counts
95 → 130
Calls
95 calls:
Slowest
691.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
381.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
328.0ms
(* (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (/ (* (* 1 1) 1) (* (* (- (* (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) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
281.0ms
(/ (* (* 1 1) 1) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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

rewrite75.0ms

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
27.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
18.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
15.0ms
(/ (cos b) (sin b))
14.0ms
(* (/ (cos b) (sin b)) (cos a))

series504.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
256.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
122.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
99.0ms
(* (/ (cos b) (sin b)) (cos a))
28.0ms
(/ (cos b) (sin b))

simplify4.1s

Counts
90 → 116
Calls
90 calls:
Slowest
348.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
332.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
323.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
316.0ms
(/ (* (* 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))))
275.0ms
(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes311.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.7s2947×body1280valid
1.6s1798×body640valid
449.0ms2151×body80valid
429.0ms745×body320valid
130.0ms362×body160valid