Details

Time bar (total: 26.5s)

sample316.0ms

Algorithm
intervals
Results
105.0ms86×body1280valid
57.0ms9×body160valid
53.0ms63×body640valid
15.0ms85×body80valid
7.0ms13×body320valid

simplify67.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
66.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize25.0ms

Local error

Found 3 expressions with local error:

4.6b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite63.0ms

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
24.0ms
(/ (* r (sin b)) (cos (+ a b)))
20.0ms
(* r (sin b))
17.0ms
(cos (+ a b))

series206.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
129.0ms
(/ (* r (sin b)) (cos (+ a b)))
53.0ms
(* r (sin b))
24.0ms
(cos (+ a b))

simplify1.6s

Counts
33 → 65
Calls
33 calls:
Slowest
327.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
274.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
262.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
236.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
213.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune670.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

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
33.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
27.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series551.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
126.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
82.0ms
(* (sin a) (sin b))
41.0ms
(* r (sin b))

simplify4.2s

Counts
56 → 102
Calls
56 calls:
Slowest
412.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
361.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
345.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
320.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
292.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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
17.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
11.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
275.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
101.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
72.0ms
(* r (sin b))
71.0ms
(* (sin a) (sin b))

simplify2.8s

Counts
46 → 90
Calls
46 calls:
Slowest
381.0ms
(/ (* (* (* 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))))))
337.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
306.0ms
(/ (* (* (* 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))))))
298.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
255.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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
28.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
22.0ms
(* (sin b) (sin a))
8.0ms
(* r (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin b) (sin a))))

series542.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
329.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
104.0ms
(fma (cos a) (cos b) (- (* (sin b) (sin a))))
56.0ms
(* r (sin b))
52.0ms
(* (sin b) (sin a))

simplify2.7s

Counts
46 → 90
Calls
46 calls:
Slowest
360.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))))
318.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))
300.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
295.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))))
281.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes378.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
3.6s2874×body1280valid
2.3s1822×body640valid
802.0ms2164×body80valid
409.0ms739×body320valid
232.0ms403×body160valid