Details

Time bar (total: 31.0s)

sample515.0ms

Algorithm
intervals
Results
275.0ms79×body1280valid
94.0ms62×body640valid
23.0ms79×body80valid
19.0ms25×body320valid
4.0ms11×body160valid

simplify106.0ms

Calls
1 calls:
Slowest
105.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize37.0ms

Local error

Found 3 expressions with local error:

3.0b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite62.0ms

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
Calls
3 calls:
Slowest
24.0ms
(/ (* r (sin b)) (cos (+ a b)))
17.0ms
(* r (sin b))
17.0ms
(cos (+ a b))

series253.0ms

Calls
3 calls:
Slowest
144.0ms
(/ (* r (sin b)) (cos (+ a b)))
69.0ms
(* r (sin b))
40.0ms
(cos (+ a b))

simplify1.6s

Calls
33 calls:
Slowest
329.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
252.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
243.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
203.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
199.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune704.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

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)))

rewrite81.0ms

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*
Calls
4 calls:
Slowest
31.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms
(* (sin a) (sin b))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* r (sin b))

series505.0ms

Calls
4 calls:
Slowest
279.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
108.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
74.0ms
(* (sin a) (sin b))
44.0ms
(* r (sin b))

simplify4.2s

Calls
56 calls:
Slowest
469.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
436.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
353.0ms
(/ (* (* (* 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)))))
330.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
318.0ms
(/ (* (* (* r r) r) (* (* (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)))))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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)))

rewrite167.0ms

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/
Calls
4 calls:
Slowest
95.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
20.0ms
(* (sin a) (sin b))

series657.0ms

Calls
4 calls:
Slowest
306.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
163.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
108.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
81.0ms
(* (sin a) (sin b))

simplify6.0s

Calls
86 calls:
Slowest
493.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
376.0ms
(/ (* (* (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)))))
355.0ms
(* (* (* 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))))))
338.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
311.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

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

rewrite45.0ms

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*
Calls
4 calls:
Slowest
21.0ms
(* r (sin b))
11.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
11.0ms
(* (sin a) (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series576.0ms

Calls
4 calls:
Slowest
345.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
116.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
67.0ms
(* (sin a) (sin b))
47.0ms
(* r (sin b))

simplify2.6s

Calls
46 calls:
Slowest
337.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
328.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (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))))))
299.0ms
(/ (* (* (* 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))))))
297.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
250.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes347.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
3.7s2880×body1280valid
1.6s1861×body640valid
921.0ms752×body320valid
914.0ms2131×body80valid
141.0ms378×body160valid