Details

Time bar (total: 38.3s)

sample782.0ms

Algorithm
intervals
Results
461.0ms25×body320valid
119.0ms92×body1280valid
57.0ms62×body640valid
12.0ms64×body80valid
6.0ms13×body160valid

simplify43.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
42.0ms
(* r (/ (sin b) (cos (+ a b))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize35.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite56.0ms

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
23.0ms
(* r (/ (sin b) (cos (+ a b))))
20.0ms
(cos (+ a b))
9.0ms
(/ (sin b) (cos (+ a b)))

series267.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
148.0ms
(* r (/ (sin b) (cos (+ a b))))
78.0ms
(/ (sin b) (cos (+ a b)))
40.0ms
(cos (+ a b))

simplify2.5s

Counts
60 → 85
Calls
60 calls:
Slowest
458.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
324.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
259.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
233.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
224.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune837.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

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

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×associate-*r*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- prod-exp frac-sub cbrt-unprod flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff associate-*r/
Counts
4 → 114
Calls
4 calls:
Slowest
106.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
32.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms
(* (sin a) (sin b))

series669.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
323.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
148.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
123.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
75.0ms
(* (sin a) (sin b))

simplify6.3s

Counts
86 → 126
Calls
86 calls:
Slowest
476.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
425.0ms
(* (* (* 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))))))
402.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
378.0ms
(+ (* (* (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 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)))))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))
0.2b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.1b
(* r (sin b))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
27×add-sqr-sqrt
23×*-un-lft-identity associate-*r* add-cube-cbrt
22×add-cbrt-cube
18×times-frac
14×pow1 prod-exp
8×associate-/r/ cbrt-unprod
7×associate-*l*
6×div-exp
5×pow-prod-down sin-mult
4×expm1-log1p-u cos-mult insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp *-commutative associate-/l*
2×flip3-- frac-sub div-inv flip-- sub-div unswap-sqr
1×clear-num frac-2neg associate-*r/ un-div-inv pow-flip inv-pow
Counts
4 → 126
Calls
4 calls:
Slowest
82.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
45.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(* r (sin b))
11.0ms
(* (sin a) (sin b))

series627.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
304.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
177.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
89.0ms
(* (sin a) (sin b))
56.0ms
(* r (sin b))

simplify7.1s

Counts
95 → 138
Calls
95 calls:
Slowest
378.0ms
(+ (* (* (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) (sin b)) (sin b))) (/ (* (* 1 1) 1) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
328.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
318.0ms
(/ (* (* 1 1) 1) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
310.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin a) (sin b))
0.2b
(/ (* (* r (sin b)) 1) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.1b
(* r (sin b))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
17×add-cbrt-cube
14×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×pow1 prod-exp
6×associate-*r* associate-*l* add-log-exp
5×div-exp cbrt-unprod sin-mult
4×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* times-frac
2×flip3-- 1-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 → 94
Calls
4 calls:
Slowest
70.0ms
(/ (* (* r (sin b)) 1) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
34.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms
(* r (sin b))
11.0ms
(* (sin a) (sin b))

series561.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
310.0ms
(/ (* (* r (sin b)) 1) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
146.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
57.0ms
(* (sin a) (sin b))
49.0ms
(* r (sin b))

simplify5.1s

Counts
61 → 106
Calls
61 calls:
Slowest
427.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
420.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
384.0ms
(/ (* (* (* (* r (sin b)) 1) (* (* r (sin b)) 1)) (* (* r (sin b)) 1)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
358.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
324.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes281.0ms

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
4.1s2836×body1280valid
2.0s1887×body640valid
481.0ms784×body320valid
456.0ms2162×body80valid
147.0ms333×body160valid