Details

Time bar (total: 26.2s)

sample451.0ms

Algorithm
intervals
Results
253.0ms89×body1280valid
52.0ms63×body640valid
44.0ms67×body80valid
17.0ms26×body320valid
3.0ms11×body160valid

simplify117.0ms

Calls
1 calls:
Slowest
116.0ms
(* r (/ (sin b) (cos (+ a b))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-inv
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp associate-*r/ *-commutative
Calls
3 calls:
Slowest
11.0ms
(/ (sin b) (cos (+ a b)))
6.0ms
(cos (+ a b))
6.0ms
(* r (/ (sin b) (cos (+ a b))))

series191.0ms

Calls
3 calls:
Slowest
102.0ms
(* r (/ (sin b) (cos (+ a b))))
64.0ms
(/ (sin b) (cos (+ a b)))
25.0ms
(cos (+ a b))

simplify1.3s

Calls
49 calls:
Slowest
238.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
186.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
173.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
137.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
38.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune774.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

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)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×associate-*r*
18×times-frac
8×add-cbrt-cube add-exp-log associate-/r/
7×sin-mult
6×pow1 cos-mult add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- associate-*l* frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-exp prod-diff pow-prod-down prod-exp associate-*r/ cbrt-unprod
Calls
4 calls:
Slowest
22.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms
(* (sin a) (sin b))

series543.0ms

Calls
4 calls:
Slowest
225.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
161.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
113.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms
(* (sin a) (sin b))

simplify4.4s

Calls
73 calls:
Slowest
476.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
388.0ms
(/ (* (* (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)))))
336.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
311.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
290.0ms
(+ (* (* (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

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
16×associate-*r*
8×add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l* associate-/l*
2×*-commutative div-inv
1×cbrt-undiv clear-num frac-2neg div-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod fma-udef sin-mult
Calls
4 calls:
Slowest
9.0ms
(* (sin a) (sin b))
8.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
4.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
1.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series516.0ms

Calls
4 calls:
Slowest
229.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
151.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
88.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
48.0ms
(* (sin a) (sin b))

simplify2.9s

Calls
60 calls:
Slowest
420.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
212.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
209.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
141.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
141.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×pow1 associate-*r* add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
3×associate-/r* times-frac associate-*l*
2×flip3-- *-commutative frac-sub flip-- sub-div
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-exp prod-diff pow-prod-down prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
25.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* (sin a) (sin b))
3.0ms
(* r (sin b))

series404.0ms

Calls
4 calls:
Slowest
220.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
85.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
57.0ms
(* (sin a) (sin b))
42.0ms
(* r (sin b))

simplify2.9s

Calls
45 calls:
Slowest
482.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
291.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
266.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
253.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
223.0ms
(/ (* (* (* 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)))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes326.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
3.7s2864×body1280valid
1.5s1846×body640valid
935.0ms743×body320valid
317.0ms2172×body80valid
156.0ms376×body160valid