Details

Time bar (total: 1.3m)

sample200.0ms

Algorithm
intervals
Results
74.0ms98×body1280valid
43.0ms70×body80valid
29.0ms51×body640valid
11.0ms29×body320valid
2.0ms8×body160valid

simplify60.0ms

Calls
1 calls:
Slowest
59.0ms
(* r (/ (sin b) (cos (+ a b))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize18.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (+ a b))
0.3b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
19×times-frac
13×associate-*r*
10×add-cbrt-cube add-exp-log
9×associate-*r/
7×associate-/l*
6×associate-/r*
5×pow1
3×expm1-log1p-u clear-num associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv cos-sum frac-2neg div-exp prod-exp un-div-inv cbrt-unprod div-inv unswap-sqr
1×+-commutative pow-prod-down *-commutative
Calls
3 calls:
Slowest
16.0ms
(* r (/ (sin b) (cos (+ a b))))
10.0ms
(/ (sin b) (cos (+ a b)))
10.0ms
(cos (+ a b))

series223.0ms

Calls
3 calls:
Slowest
138.0ms
(* r (/ (sin b) (cos (+ a b))))
51.0ms
(/ (sin b) (cos (+ a b)))
33.0ms
(cos (+ a b))

simplify2.6s

Calls
71 calls:
Slowest
434.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
304.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
292.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
229.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
223.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

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)))

rewrite538.0ms

Algorithm
rewrite-expression-head
Rules
280×add-sqr-sqrt
188×*-un-lft-identity
144×prod-diff
119×associate-*r*
117×associate-*l*
115×add-cube-cbrt
67×times-frac
64×unswap-sqr
36×distribute-lft-out-- difference-of-squares
27×*-commutative
22×associate-/r*
17×associate-*r/
13×add-cbrt-cube add-exp-log
12×fma-neg
8×pow1 associate-/r/
7×sin-mult associate-/l*
6×cos-mult add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×clear-num flip3-- prod-exp frac-sub cbrt-unprod flip-- sub-div
2×cbrt-undiv frac-2neg div-exp pow-prod-down un-div-inv div-inv
1×sub-neg diff-log
Calls
4 calls:
Slowest
313.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
121.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
80.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))

series669.0ms

Calls
4 calls:
Slowest
314.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
176.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
110.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms
(* (sin a) (sin b))

simplify40.8s

Calls
491 calls:
Slowest
464.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
425.0ms
(/ (sqrt (sin b)) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
425.0ms
(* (* (* 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))))))
412.0ms
(/ (* (* (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)))))
396.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune4.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
25×*-un-lft-identity
24×add-cube-cbrt
19×times-frac
16×associate-*r*
13×add-cbrt-cube add-exp-log
9×associate-*r/
8×pow1
7×associate-/l*
6×associate-/r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num prod-exp cbrt-unprod unswap-sqr
2×cbrt-undiv frac-2neg div-exp pow-prod-down un-div-inv *-commutative div-inv
1×fma-udef sin-mult
Calls
4 calls:
Slowest
20.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
15.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
12.0ms
(* (sin a) (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series666.0ms

Calls
4 calls:
Slowest
318.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
161.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
119.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
68.0ms
(* (sin a) (sin b))

simplify5.2s

Calls
83 calls:
Slowest
432.0ms
(* (* (* 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)))))))
383.0ms
(/ (* (* (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))))))
293.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
279.0ms
(* (* (* 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)))))))
264.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
25×*-un-lft-identity
24×add-cube-cbrt
19×times-frac
16×associate-*r*
13×add-cbrt-cube add-exp-log
9×associate-*r/
8×pow1
7×associate-/l*
6×associate-/r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num prod-exp cbrt-unprod unswap-sqr
2×cbrt-undiv frac-2neg div-exp pow-prod-down un-div-inv *-commutative div-inv
1×fma-udef sin-mult
Calls
4 calls:
Slowest
19.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
14.0ms
(* (sin a) (sin b))
13.0ms
(/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
0.0ms
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))

series1.3s

Calls
4 calls:
Slowest
618.0ms
(/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
409.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
197.0ms
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
82.0ms
(* (sin a) (sin b))

simplify5.4s

Calls
83 calls:
Slowest
342.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
341.0ms
(/ (* (* (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))))))))
340.0ms
(* (* (* r r) r) (* (* (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))) (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))) (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))))
320.0ms
(* (* (* 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)))))))))
244.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes403.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.1s3020×body1280valid
1.9s1778×body640valid
495.0ms792×body320valid
465.0ms2079×body80valid
118.0ms332×body160valid