Details

Time bar (total: 42.9s)

sample490.0ms

Algorithm
intervals
Results
231.0ms103×body1280valid
46.0ms59×body640valid
43.0ms64×body80valid
12.0ms22×body320valid
4.0ms8×body160valid

simplify41.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
40.0ms
(* r (/ (sin b) (cos (+ a b))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize36.0ms

Local error

Found 3 expressions with local error:

2.2b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite32.0ms

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

series183.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
106.0ms
(* r (/ (sin b) (cos (+ a b))))
49.0ms
(/ (sin b) (cos (+ a b)))
28.0ms
(cos (+ a b))

simplify2.6s

Counts
60 → 85
Calls
60 calls:
Slowest
468.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
286.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
254.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
240.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
232.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

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))

rewrite203.0ms

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
139.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
32.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms
(* (sin a) (sin b))
10.0ms
(* (cos a) (cos b))

series585.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
296.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
148.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
83.0ms
(* (sin a) (sin b))
57.0ms
(* (cos a) (cos b))

simplify5.9s

Counts
90 → 129
Calls
90 calls:
Slowest
415.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
375.0ms
(+ (* (* (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 a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
356.0ms
(* (* (* 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))))))
348.0ms
(/ (* (* (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)))))

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(expm1 (* (cos a) (cos b)))
0.3b
(/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b))))
0.3b
(log1p (expm1 (* (cos a) (cos b))))
0.2b
(* (sin a) (sin b))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
9×times-frac
8×add-cbrt-cube add-exp-log
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×associate-/r/
1×cbrt-undiv log1p-udef expm1-log1p clear-num frac-2neg flip3-- div-exp pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod div-inv flip-- sin-mult expm1-udef unswap-sqr
Counts
4 → 78
Calls
4 calls:
Slowest
15.0ms
(/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b))))
10.0ms
(* (sin a) (sin b))
0.0ms
(expm1 (* (cos a) (cos b)))
0.0ms
(log1p (expm1 (* (cos a) (cos b))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(/ (sin b) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b))))
105.0ms
(log1p (expm1 (* (cos a) (cos b))))
101.0ms
(expm1 (* (cos a) (cos b)))
79.0ms
(* (sin a) (sin b))

simplify3.5s

Counts
52 → 90
Calls
52 calls:
Slowest
403.0ms
(+ (* (log1p (expm1 (* (cos a) (cos b)))) (log1p (expm1 (* (cos a) (cos b))))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b)))))
360.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
328.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b))) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b)))) (- (log1p (expm1 (* (cos a) (cos b)))) (* (sin a) (sin b)))))
302.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* 1/2 (pow b 2))))
247.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

23.5b
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b
(/ (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))

rewrite310.0ms

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
143.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
112.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
41.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))

series377.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
95.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
66.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
57.0ms
(* (sin a) (sin b))

simplify13.7s

Counts
103 → 133
Calls
103 calls:
Slowest
923.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
642.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
468.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))
434.0ms
(/ (* (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))))))))
417.0ms
(/ (cbrt (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))

prune2.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes367.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.6s2972×body1280valid
1.5s1821×body640valid
446.0ms2118×body80valid
415.0ms726×body320valid
161.0ms364×body160valid