Details

Time bar (total: 39.9s)

sample1.2s

Algorithm
intervals
Results
888.0ms95×body1280valid
60.0ms59×body640valid
15.0ms71×body80valid
15.0ms20×body320valid
6.0ms11×body160valid

simplify58.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
57.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize37.0ms

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))

rewrite79.0ms

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×associate-/r* times-frac associate-*r* associate-*l* insert-posit16 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 → 50
Calls
3 calls:
Slowest
36.0ms
(cos (+ a b))
23.0ms
(/ (* r (sin b)) (cos (+ a b)))
16.0ms
(* r (sin b))

series261.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
161.0ms
(/ (* r (sin b)) (cos (+ a b)))
54.0ms
(* r (sin b))
45.0ms
(cos (+ a b))

simplify1.4s

Counts
33 → 59
Calls
33 calls:
Slowest
358.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
207.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
195.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
168.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
159.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune589.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

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))

rewrite112.0ms

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×prod-exp associate-/r/ cbrt-unprod insert-posit16 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 → 85
Calls
4 calls:
Slowest
52.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms
(* (cos a) (cos b))
21.0ms
(* (sin a) (sin b))
16.0ms
(* r (sin b))

series472.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
85.0ms
(* (sin a) (sin b))
59.0ms
(* (cos a) (cos b))
41.0ms
(* r (sin b))

simplify3.2s

Counts
60 → 97
Calls
60 calls:
Slowest
352.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
332.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
319.0ms
(/ (* (* (* 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)))))
293.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
286.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite197.0ms

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×prod-exp cbrt-unprod insert-posit16 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 → 109
Calls
4 calls:
Slowest
134.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
27.0ms
(* (sin a) (sin b))
26.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms
(* (cos a) (cos b))

series590.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
291.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
142.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
82.0ms
(* (sin a) (sin b))
75.0ms
(* (cos a) (cos b))

simplify5.3s

Counts
90 → 121
Calls
90 calls:
Slowest
401.0ms
(* (* (* 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))))))
357.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
342.0ms
(/ (* (* (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)))))
340.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
303.0ms
(+ (* (* (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

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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)))))))

rewrite120.0ms

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×associate-/r/ insert-posit16
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 → 100
Calls
4 calls:
Slowest
63.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
29.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
16.0ms
(log (exp (* (sin a) (sin b))))
10.0ms
(* (sin a) (sin b))

series672.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
330.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
180.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
83.0ms
(* (sin a) (sin b))
79.0ms
(log (exp (* (sin a) (sin b))))

simplify12.7s

Counts
83 → 112
Calls
83 calls:
Slowest
402.0ms
(/ (* (* (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)))))))
373.0ms
(+ (* (* (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)))))))
372.0ms
(* (* (* 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))))))))
358.0ms
(+ (* (* (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)))))))
332.0ms
(* (* (* (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

regimes343.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.8s2987×body1280valid
2.0s1863×body640valid
801.0ms741×body320valid
465.0ms2068×body80valid
119.0ms342×body160valid