Details

Time bar (total: 42.1s)

sample660.0ms

Algorithm
intervals
Results
456.0ms71×body80valid
75.0ms95×body1280valid
30.0ms59×body640valid
7.0ms20×body320valid
3.0ms11×body160valid

simplify50.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
49.0ms
(* r (/ (sin b) (cos (+ a b))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize36.0ms

Local error

Found 3 expressions with local error:

4.2b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.1b
(* r (/ (sin b) (cos (+ a b))))

rewrite55.0ms

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
29.0ms
(cos (+ a b))
13.0ms
(* r (/ (sin b) (cos (+ a b))))
9.0ms
(/ (sin b) (cos (+ a b)))

series223.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
135.0ms
(* r (/ (sin b) (cos (+ a b))))
60.0ms
(/ (sin b) (cos (+ a b)))
28.0ms
(cos (+ a b))

simplify2.4s

Counts
60 → 85
Calls
60 calls:
Slowest
450.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
345.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
270.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
243.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
234.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
23×associate-*r*
19×times-frac
15×add-cbrt-cube add-exp-log
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r* pow-prod-down *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub div-inv flip-- sub-div
1×clear-num frac-2neg associate-*r/
Counts
4 → 117
Calls
4 calls:
Slowest
88.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
38.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(* (cos a) (cos b))
11.0ms
(* (sin a) (sin b))

series558.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
277.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
163.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
66.0ms
(* (sin a) (sin b))
51.0ms
(* (cos a) (cos b))

simplify5.7s

Counts
90 → 129
Calls
90 calls:
Slowest
424.0ms
(/ (* (* (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)))))
382.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
367.0ms
(* (* (* 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))))))
359.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
327.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
12×*-un-lft-identity add-cube-cbrt
10×pow1
9×associate-*r* associate-*l*
4×expm1-log1p-u prod-exp associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac pow-prod-down cos-mult *-commutative sin-mult unswap-sqr
2×cbrt-undiv div-exp
1×clear-num frac-2neg flip3-- frac-sub div-inv flip-- associate-/l* sub-div
Counts
4 → 93
Calls
4 calls:
Slowest
50.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
18.0ms
(* (cos a) (cos b))
16.0ms
(* r (sin b))

series467.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
56.0ms
(* (sin a) (sin b))
53.0ms
(* (cos a) (cos b))
41.0ms
(* r (sin b))

simplify3.6s

Counts
60 → 105
Calls
60 calls:
Slowest
375.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
373.0ms
(/ (* (* (* 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)))))
350.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
344.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
302.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* 1/2 (pow b 2))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

25.0b
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))

rewrite380.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
29×sin-mult
20×add-cbrt-cube add-exp-log
18×pow-prod-down
16×add-sqr-sqrt
14×cbrt-div *-un-lft-identity add-cube-cbrt
11×frac-times associate-*l/
9×times-frac prod-exp associate-/r/ cbrt-unprod
7×associate-*r/ cos-mult frac-sub
4×expm1-log1p-u associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×pow-plus *-commutative
1×cbrt-prod pow2 cbrt-undiv clear-num frac-2neg flip3-- pow1/3 swap-sqr div-exp pow3 rem-cbrt-cube div-inv flip-- unswap-sqr
Counts
4 → 121
Calls
4 calls:
Slowest
153.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
152.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
59.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
14.0ms
(* (sin a) (sin b))

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
74.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
54.0ms
(* (sin a) (sin b))
51.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify12.6s

Counts
103 → 133
Calls
103 calls:
Slowest
846.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
724.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
412.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))
397.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))))
397.0ms
(- (log (sin b)) (log (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes365.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.1s2987×body1280valid
2.3s1863×body640valid
538.0ms2068×body80valid
449.0ms741×body320valid
144.0ms342×body160valid