Details

Time bar (total: 25.9s)

sample314.0ms

Algorithm
intervals
Results
92.0ms88×body1280valid
69.0ms64×body640valid
15.0ms72×body80valid
11.0ms22×body320valid
3.0ms10×body160valid

simplify39.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
39.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize34.0ms

Local error

Found 3 expressions with local error:

4.4b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.2b
(* r (sin b))

rewrite58.0ms

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×expm1-log1p-u associate-/r* times-frac associate-*r* associate-*l* insert-posit16 log1p-expm1-u 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 → 56
Calls
3 calls:
Slowest
30.0ms
(cos (+ a b))
18.0ms
(/ (* r (sin b)) (cos (+ a b)))
8.0ms
(* r (sin b))

series220.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
135.0ms
(/ (* r (sin b)) (cos (+ a b)))
56.0ms
(* r (sin b))
29.0ms
(cos (+ a b))

simplify1.4s

Counts
33 → 65
Calls
33 calls:
Slowest
307.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
234.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
229.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
204.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
183.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune619.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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

rewrite75.0ms

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×expm1-log1p-u associate-/r/ cos-mult 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 → 90
Calls
4 calls:
Slowest
26.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(* r (sin b))

series519.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
132.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms
(* r (sin b))
49.0ms
(* (sin a) (sin b))

simplify4.0s

Counts
56 → 102
Calls
56 calls:
Slowest
364.0ms
(+ (* (* (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
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
340.0ms
(/ (* (* (* 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)))))
338.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
311.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

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*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative unswap-sqr
1×clear-num frac-2neg fma-udef div-inv sin-mult associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
22.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
21.0ms
(* (sin a) (sin b))
16.0ms
(* r (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
130.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
69.0ms
(* (sin a) (sin b))
66.0ms
(* r (sin b))

simplify2.6s

Counts
46 → 90
Calls
46 calls:
Slowest
309.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
309.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (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))))))
297.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
278.0ms
(/ (* (* (* 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))))))
228.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* r (sin b)) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
0.2b
(* (sin a) (sin b))
0.2b
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
0.2b
(* r (sin b))

rewrite32.0ms

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*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative unswap-sqr
1×clear-num frac-2neg fma-udef div-inv sin-mult associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
11.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
10.0ms
(* (sin a) (sin b))
9.0ms
(* r (sin b))
0.0ms
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))

series732.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
428.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
161.0ms
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
81.0ms
(* (sin a) (sin b))
62.0ms
(* r (sin b))

simplify2.9s

Counts
46 → 90
Calls
46 calls:
Slowest
403.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
402.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
307.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
292.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
240.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes325.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.6s2947×body1280valid
2.3s1798×body640valid
493.0ms745×body320valid
446.0ms2151×body80valid
128.0ms362×body160valid