Details

Time bar (total: 42.2s)

sample752.0ms

Algorithm
intervals
Results
548.0ms95×body1280valid
48.0ms59×body640valid
18.0ms71×body80valid
11.0ms20×body320valid
5.0ms11×body160valid

simplify58.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
58.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize32.0ms

Local error

Found 3 expressions with local error:

4.2b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* 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
19.0ms
(/ (* r (sin b)) (cos (+ a b)))
19.0ms
(cos (+ a b))
18.0ms
(* r (sin b))

series251.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
163.0ms
(/ (* r (sin b)) (cos (+ a b)))
54.0ms
(* r (sin b))
33.0ms
(cos (+ a b))

simplify1.6s

Counts
33 → 65
Calls
33 calls:
Slowest
282.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
252.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
239.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
234.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
223.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune647.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

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))

rewrite76.0ms

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
40.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms
(* (sin a) (sin b))
10.0ms
(* (cos a) (cos b))
8.0ms
(* r (sin b))

series470.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
274.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
71.0ms
(* (cos a) (cos b))
70.0ms
(* (sin a) (sin b))
55.0ms
(* r (sin b))

simplify3.4s

Counts
60 → 105
Calls
60 calls:
Slowest
349.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
336.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
319.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
305.0ms
(/ (* (* (* 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)))))
301.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

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))

rewrite176.0ms

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
112.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
27.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms
(* (cos a) (cos b))
16.0ms
(* (sin a) (sin b))

series576.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
327.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
145.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
54.0ms
(* (sin a) (sin b))
49.0ms
(* (cos a) (cos b))

simplify5.8s

Counts
90 → 129
Calls
90 calls:
Slowest
399.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
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)))))
360.0ms
(* (* (* 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))))))
353.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
351.0ms
(/ (* (* (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)))))

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

2.9b
(log (exp (* (sin a) (sin b))))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
19×times-frac
18×associate-*r*
13×add-cbrt-cube add-exp-log
9×pow1
6×associate-*l*
5×add-log-exp
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u
3×log-prod associate-/r* prod-exp log-pow cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative div-inv flip--
1×exp-prod clear-num frac-2neg exp-to-pow rem-log-exp associate-*r/ sin-mult
Counts
4 → 108
Calls
4 calls:
Slowest
68.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
22.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
11.0ms
(* (sin a) (sin b))
10.0ms
(log (exp (* (sin a) (sin b))))

series653.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
182.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
81.0ms
(* (sin a) (sin b))
61.0ms
(log (exp (* (sin a) (sin b))))

simplify14.5s

Counts
83 → 120
Calls
83 calls:
Slowest
509.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
498.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))
446.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
409.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
371.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes383.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.1s2987×body1280valid
2.0s1863×body640valid
625.0ms741×body320valid
371.0ms2068×body80valid
188.0ms342×body160valid