Details

Time bar (total: 37.4s)

sample291.0ms

Algorithm
intervals
Results
107.0ms88×body1280valid
35.0ms66×body640valid
14.0ms27×body320valid
8.0ms66×body80valid
2.0ms9×body160valid

simplify34.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
34.0ms
(* r (/ (sin b) (cos (+ a b))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize34.0ms

Local error

Found 3 expressions with local error:

3.5b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 76
Calls
3 calls:
Slowest
13.0ms
(* r (/ (sin b) (cos (+ a b))))
10.0ms
(/ (sin b) (cos (+ a b)))
9.0ms
(cos (+ a b))

series228.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
114.0ms
(* r (/ (sin b) (cos (+ a b))))
73.0ms
(/ (sin b) (cos (+ a b)))
40.0ms
(cos (+ a b))

simplify2.4s

Counts
60 → 85
Calls
60 calls:
Slowest
420.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
269.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
266.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
224.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
205.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune878.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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)))

rewrite160.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u
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 fma-neg diff-log prod-diff associate-*r/
Counts
4 → 114
Calls
4 calls:
Slowest
91.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
40.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))

series733.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
312.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
181.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
154.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
85.0ms
(* (sin a) (sin b))

simplify6.9s

Counts
86 → 126
Calls
86 calls:
Slowest
639.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
540.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
402.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
370.0ms
(* (* (* 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))))))
357.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
0.1b
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
19×times-frac
18×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
7×add-log-exp
6×associate-*l*
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- prod-diff prod-exp cbrt-unprod flip-- associate-/l* unswap-sqr
2×cbrt-undiv diff-log div-exp pow-prod-down *-commutative div-inv
1×log1p-udef clear-num sub-neg frac-2neg fma-neg associate-*r/ sin-mult
Counts
4 → 111
Calls
4 calls:
Slowest
66.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
39.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
29.0ms
(* (sin a) (sin b))
11.0ms
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))

series790.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
325.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
221.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
180.0ms
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
64.0ms
(* (sin a) (sin b))

simplify6.9s

Counts
86 → 123
Calls
86 calls:
Slowest
890.0ms
(/ (exp (* (cos a) (cos b))) (exp (log1p (expm1 (* (sin a) (sin b))))))
419.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
366.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))) (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))) (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))))
359.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
349.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log1p (expm1 (* (sin a) (sin b)))) (log1p (expm1 (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

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))

rewrite137.0ms

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×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv associate-/l*
Counts
4 → 91
Calls
4 calls:
Slowest
61.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
35.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms
(* (sin a) (sin b))
19.0ms
(* (cos a) (cos b))

series644.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
360.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
149.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
80.0ms
(* (cos a) (cos b))
54.0ms
(* (sin a) (sin b))

simplify4.5s

Counts
57 → 103
Calls
57 calls:
Slowest
501.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
411.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
397.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
369.0ms
(/ (* (* (* 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)))))
312.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes256.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.5s2964×body1280valid
1.6s1793×body640valid
508.0ms777×body320valid
436.0ms2112×body80valid
156.0ms355×body160valid