Details

Time bar (total: 38.1s)

sample342.0ms

Algorithm
intervals
Results
191.0ms88×body1280valid
41.0ms64×body640valid
13.0ms72×body80valid
10.0ms22×body320valid
4.0ms10×body160valid

simplify166.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
165.0ms
(* r (/ (sin b) (cos (+ a b))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite287.0ms

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
146.0ms
(* r (/ (sin b) (cos (+ a b))))
85.0ms
(/ (sin b) (cos (+ a b)))
20.0ms
(cos (+ a b))

series414.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
173.0ms
(* r (/ (sin b) (cos (+ a b))))
159.0ms
(/ (sin b) (cos (+ a b)))
82.0ms
(cos (+ a b))

simplify2.5s

Counts
60 → 85
Calls
60 calls:
Slowest
486.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
317.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
242.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
240.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
219.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune906.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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)))

rewrite161.0ms

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
101.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
25.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms
(* (sin a) (sin b))

series658.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
314.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
160.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
68.0ms
(* (sin a) (sin b))

simplify6.0s

Counts
86 → 126
Calls
86 calls:
Slowest
424.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
413.0ms
(* (* (* 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))))))
384.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
357.0ms
(/ (* (* (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)))))
347.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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))))))
0.2b
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
19×times-frac
16×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
6×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num frac-2neg associate-*r/ fma-udef sin-mult
Counts
4 → 98
Calls
4 calls:
Slowest
24.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
11.0ms
(* (sin a) (sin b))
8.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series735.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
321.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
193.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
151.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
70.0ms
(* (sin a) (sin b))

simplify4.7s

Counts
73 → 110
Calls
73 calls:
Slowest
478.0ms
(* (* (* r r) r) (* (* (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))) (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))))
406.0ms
(/ (* (* (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))))))
333.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
310.0ms
(* (* (* r r) r) (/ (* (* (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)))))))
260.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

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×expm1-log1p-u cos-mult insert-posit16 log1p-expm1-u 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 → 126
Calls
4 calls:
Slowest
89.0ms
(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
52.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
17.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series559.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
308.0ms
(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
138.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
70.0ms
(* (sin a) (sin b))
44.0ms
(* r (sin b))

simplify7.0s

Counts
95 → 138
Calls
95 calls:
Slowest
384.0ms
(* (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (/ (* (* 1 1) 1) (* (* (- (* (cos b) (cos a)) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
380.0ms
(* (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (/ (* (* 1 1) 1) (* (* (- (* (cos b) (cos a)) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
362.0ms
(/ (* (* 1 1) 1) (* (* (- (* (cos b) (cos a)) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
361.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
312.0ms
(+ (* (* (cos b) (cos a)) (* (cos b) (cos a))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos b) (cos a)) (* (sin a) (sin b)))))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes359.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.4s2947×body1280valid
1.9s1798×body640valid
457.0ms745×body320valid
444.0ms2151×body80valid
202.0ms362×body160valid