Details

Time bar (total: 44.7s)

sample563.0ms

Algorithm
intervals
Results
378.0ms62×body640valid
79.0ms92×body1280valid
10.0ms25×body320valid
8.0ms64×body80valid
3.0ms13×body160valid

simplify28.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
28.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize18.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite57.0ms

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
20.0ms
(cos (+ a b))
17.0ms
(* r (sin b))
16.0ms
(/ (* r (sin b)) (cos (+ a b)))

series344.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
169.0ms
(/ (* r (sin b)) (cos (+ a b)))
135.0ms
(* r (sin b))
39.0ms
(cos (+ a b))

simplify1.5s

Counts
33 → 59
Calls
33 calls:
Slowest
289.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
265.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
196.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
185.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
152.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune672.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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
55.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms
(* r (sin b))
13.0ms
(* (sin a) (sin b))

series626.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
361.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
142.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms
(* r (sin b))
57.0ms
(* (sin a) (sin b))

simplify3.6s

Counts
53 → 92
Calls
53 calls:
Slowest
359.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
353.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
326.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
315.0ms
(/ (* (* (* 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)))))
303.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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

rewrite103.0ms

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
36.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
31.0ms
(* (/ (cos b) (sin b)) (cos a))
21.0ms
(/ (cos b) (sin b))
14.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))

series542.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
298.0ms
(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
127.0ms
(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
91.0ms
(* (/ (cos b) (sin b)) (cos a))
25.0ms
(/ (cos b) (sin b))

simplify4.4s

Counts
90 → 116
Calls
90 calls:
Slowest
376.0ms
(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))
362.0ms
(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
357.0ms
(/ (* (* (cos b) (cos b)) (cos b)) (* (* (sin b) (sin b)) (sin b)))
305.0ms
(/ (* (* 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))))
252.0ms
(/ (exp (* (/ (cos b) (sin b)) (cos a))) (exp (sin a)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
35×pow-prod-down
32×add-cbrt-cube add-exp-log
24×sin-mult
23×cos-mult
17×add-sqr-sqrt prod-exp cbrt-unprod
16×associate-/l/
15×*-un-lft-identity add-cube-cbrt
12×times-frac associate-*l/ associate-*r/
10×frac-times
9×frac-sub
8×pow-sqr pow-prod-up
5×associate-*r* associate-*l* sub-div
4×pow-plus insert-posit16 associate-/l* add-log-exp difference-of-squares
3×associate-/r* associate-/r/ *-commutative
2×pow2 swap-sqr
1×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-sub div-exp frac-add flip-+ div-inv flip-- unswap-sqr
Counts
4 → 148
Calls
4 calls:
Slowest
180.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
75.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
60.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
22.0ms
(* (sin a) (sin b))

series497.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
300.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
77.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
66.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
54.0ms
(* (sin a) (sin b))

simplify18.7s

Counts
149 → 160
Calls
149 calls:
Slowest
901.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
833.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
729.0ms
(* (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))))
696.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
564.0ms
(/ (* (* (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (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)))))

prune2.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes646.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
3.7s2836×body1280valid
1.9s1887×body640valid
464.0ms784×body320valid
361.0ms2162×body80valid
111.0ms333×body160valid