Details

Time bar (total: 25.1s)

sample319.0ms

Algorithm
intervals
Results
103.0ms90×body1280valid
90.0ms68×body640valid
15.0ms60×body80valid
12.0ms24×body320valid
6.0ms14×body160valid

simplify70.0ms

Counts
1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize34.0ms

Local error

Found 3 expressions with local error:

2.7b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite76.0ms

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
33.0ms
(cos (+ a b))
23.0ms
(/ (* r (sin b)) (cos (+ a b)))
17.0ms
(* r (sin b))

series266.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
159.0ms
(/ (* r (sin b)) (cos (+ a b)))
66.0ms
(* r (sin b))
41.0ms
(cos (+ a b))

simplify922.0ms

Counts
65 → 65

prune782.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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)) (* (sin a) (sin b)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
Slowest
40.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
36.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms
(* r (sin b))
14.0ms
(* (sin a) (sin b))

series598.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
349.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
122.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms
(* r (sin b))
57.0ms
(* (sin a) (sin b))

simplify1.8s

Counts
102 → 102

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative unswap-sqr
1×clear-num frac-2neg fma-udef div-inv sin-mult associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
24.0ms
(* (sin a) (sin b))
24.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
16.0ms
(* r (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
479.0ms
(* r (sin b))
326.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
131.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
69.0ms
(* (sin a) (sin b))

simplify1.5s

Counts
90 → 90

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.2b
(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

rewrite454.0ms

Algorithm
rewrite-expression-head
Rules
82×pow1
55×times-frac
42×add-cbrt-cube add-exp-log
34×pow-prod-down
29×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
25×cos-mult sin-mult
22×associate-/r*
18×prod-exp cbrt-unprod
16×associate-/l/
12×associate-*l/ associate-*r/
10×frac-times associate-/r/ difference-of-squares
9×frac-sub
8×pow-sqr pow-prod-up
7×cbrt-undiv div-exp
5×associate-/l* sub-div
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u div-inv add-log-exp
3×flip3-+ frac-add flip-+
2×pow2 clear-num frac-2neg swap-sqr associate-*r* associate-*l* *-commutative
1×flip3-- div-sub flip--
Counts
4 → 195
Calls
4 calls:
Slowest
221.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
84.0ms
(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
74.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
69.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
594.0ms
(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
273.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
78.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
67.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

simplify1.7s

Counts
207 → 207

prune3.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes376.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch7.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.5s2903×body1280valid
1.7s1956×body640valid
507.0ms756×body320valid
384.0ms2016×body80valid
136.0ms370×body160valid