Details

Time bar (total: 28.8s)

sample279.0ms

Algorithm
intervals
Results
145.0ms98×body1280valid
47.0ms62×body640valid
10.0ms69×body80valid
9.0ms18×body320valid
3.0ms9×body160valid

simplify82.0ms

Calls
1 calls:
Slowest
81.0ms
(* r (/ (sin b) (cos (+ a b))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize35.0ms

Local error

Found 3 expressions with local error:

2.8b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.1b
(* r (/ (sin b) (cos (+ a b))))

rewrite20.0ms

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
8.0ms
(/ (sin b) (cos (+ a b)))
6.0ms
(cos (+ a b))
3.0ms
(* r (/ (sin b) (cos (+ a b))))

series229.0ms

Calls
3 calls:
Slowest
145.0ms
(* r (/ (sin b) (cos (+ a b))))
46.0ms
(/ (sin b) (cos (+ a b)))
38.0ms
(cos (+ a b))

simplify1.4s

Calls
49 calls:
Slowest
242.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
190.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
182.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
153.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
47.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune873.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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
14.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* (sin a) (sin b))

series654.0ms

Calls
4 calls:
Slowest
326.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
155.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
58.0ms
(* (sin a) (sin b))

simplify4.3s

Calls
73 calls:
Slowest
468.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
394.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
384.0ms
(/ (* (* (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)))))
313.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
279.0ms
(+ (* (* (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: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
11×associate-*r* add-exp-log
9×pow1
8×add-sqr-sqrt *-un-lft-identity add-cbrt-cube associate-/r/ add-cube-cbrt
7×sin-mult
6×cos-mult add-log-exp
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- prod-exp frac-sub flip-- sub-div
2×rec-exp pow-prod-down *-commutative cbrt-unprod div-inv
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff associate-*r/ un-div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
30.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* (sin a) (sin b))

series574.0ms

Calls
4 calls:
Slowest
259.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
147.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
107.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
61.0ms
(* (sin a) (sin b))

simplify4.6s

Calls
48 calls:
Slowest
1.2s
(* (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
498.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
349.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
332.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
317.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (* r (sin b)) 1) (- (* (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
(* r (sin b))

rewrite57.0ms

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
26.0ms
(/ (* (* r (sin b)) 1) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* (sin a) (sin b))
3.0ms
(* r (sin b))

series544.0ms

Calls
4 calls:
Slowest
328.0ms
(/ (* (* r (sin b)) 1) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
110.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
55.0ms
(* (sin a) (sin b))
51.0ms
(* r (sin b))

simplify3.1s

Calls
46 calls:
Slowest
455.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
348.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
311.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
303.0ms
(/ (* (* (* (* r (sin b)) 1) (* (* r (sin b)) 1)) (* (* r (sin b)) 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)))))
258.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes289.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.2s2948×body1280valid
1.7s1840×body640valid
837.0ms782×body320valid
405.0ms2096×body80valid
120.0ms336×body160valid