Details

Time bar (total: 23.0s)

sample593.0ms

Algorithm
intervals
Results
271.0ms89×body1280valid
134.0ms63×body640valid
17.0ms26×body320valid
16.0ms67×body80valid
6.0ms11×body160valid

simplify102.0ms

Calls
1 calls:
Slowest
101.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize39.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* times-frac associate-*r* insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp *-commutative div-inv associate-/l*
Calls
3 calls:
Slowest
11.0ms
(/ (* r (sin b)) (cos (+ a b)))
10.0ms
(cos (+ a b))
3.0ms
(* r (sin b))

series322.0ms

Calls
3 calls:
Slowest
204.0ms
(/ (* r (sin b)) (cos (+ a b)))
81.0ms
(* r (sin b))
36.0ms
(cos (+ a b))

simplify628.0ms

Calls
24 calls:
Slowest
157.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
143.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
109.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
60.0ms
(- (log (* r (sin b))) (log (cos (+ a b))))
47.0ms
(/ (* (sin b) r) (cos (+ a b)))

prune646.0ms

Pruning

8 alts after pruning (8 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)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×pow1 associate-*r* add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
3×associate-/r* times-frac associate-*l*
2×flip3-- *-commutative frac-sub flip-- sub-div
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-exp prod-diff pow-prod-down prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
29.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* (sin a) (sin b))
3.0ms
(* r (sin b))

series433.0ms

Calls
4 calls:
Slowest
224.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
104.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
68.0ms
(* (sin a) (sin b))
36.0ms
(* r (sin b))

simplify2.7s

Calls
45 calls:
Slowest
453.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
300.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
290.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
259.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
224.0ms
(/ (* (* (* 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)))))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×pow1 associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac associate-*l*
2×*-commutative
1×cbrt-undiv clear-num frac-2neg div-exp pow-prod-down prod-exp cbrt-unprod fma-udef div-inv sin-mult associate-/l*
Calls
4 calls:
Slowest
10.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
9.0ms
(* (sin a) (sin b))
6.0ms
(* r (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series425.0ms

Calls
4 calls:
Slowest
251.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
84.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
50.0ms
(* (sin a) (sin b))
40.0ms
(* r (sin b))

simplify1.6s

Calls
35 calls:
Slowest
257.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
236.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
182.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
150.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
133.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ r (/ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(/ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (sin b))
0.1b
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
16×associate-/r*
8×add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* div-inv associate-/l*
2×clear-num frac-2neg
1×cbrt-undiv div-exp pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod fma-udef sin-mult
Calls
4 calls:
Slowest
9.0ms
(* (sin a) (sin b))
8.0ms
(/ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (sin b))
2.0ms
(/ r (/ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (sin b)))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series566.0ms

Calls
4 calls:
Slowest
273.0ms
(/ r (/ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (sin b)))
124.0ms
(/ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (sin b))
98.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
72.0ms
(* (sin a) (sin b))

simplify3.5s

Calls
60 calls:
Slowest
396.0ms
(/ (* (* (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (* (* (sin b) (sin b)) (sin b)))
239.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
205.0ms
(- (/ 1 b) (+ a (* 1/2 (/ (pow a 2) b))))
183.0ms
(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b))
168.0ms
(+ (* 1/2 (* (pow a 2) (* r b))) (+ (* a (* r (pow b 2))) (* r b)))

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes335.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
4.4s2864×body1280valid
1.6s1846×body640valid
447.0ms2172×body80valid
367.0ms743×body320valid
184.0ms376×body160valid