Details

Time bar (total: 27.7s)

sample405.0ms

Algorithm
intervals
Results
178.0ms91×body1280valid
41.0ms66×body640valid
13.0ms25×body320valid
9.0ms64×body80valid
3.0ms10×body160valid

simplify68.0ms

Calls
1 calls:
Slowest
67.0ms
(* r (/ (sin b) (cos (+ a b))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize30.0ms

Local error

Found 3 expressions with local error:

3.2b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-inv
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp associate-*r/ *-commutative
Calls
3 calls:
Slowest
5.0ms
(/ (sin b) (cos (+ a b)))
3.0ms
(cos (+ a b))
3.0ms
(* r (/ (sin b) (cos (+ a b))))

series241.0ms

Calls
3 calls:
Slowest
136.0ms
(* r (/ (sin b) (cos (+ a b))))
66.0ms
(/ (sin b) (cos (+ a b)))
40.0ms
(cos (+ a b))

simplify1.3s

Calls
49 calls:
Slowest
222.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
179.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
177.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
172.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
44.0ms
(/ (* (sin b) r) (cos (+ a b)))

prune766.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

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)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×associate-*r*
18×times-frac
8×add-cbrt-cube add-exp-log associate-/r/
7×sin-mult
6×pow1 cos-mult add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- associate-*l* frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-exp prod-diff pow-prod-down prod-exp associate-*r/ cbrt-unprod
Calls
4 calls:
Slowest
17.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
13.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms
(* (sin a) (sin b))

series667.0ms

Calls
4 calls:
Slowest
314.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
171.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
115.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms
(* (sin a) (sin b))

simplify4.5s

Calls
73 calls:
Slowest
440.0ms
(/ (* (* (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)))))
435.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
337.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
318.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
316.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

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* associate-/l*
2×*-commutative div-inv
1×cbrt-undiv clear-num frac-2neg div-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod fma-udef sin-mult
Calls
4 calls:
Slowest
9.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
6.0ms
(* (sin a) (sin b))
2.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series678.0ms

Calls
4 calls:
Slowest
317.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
148.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
147.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
65.0ms
(* (sin a) (sin b))

simplify3.0s

Calls
60 calls:
Slowest
402.0ms
(/ (* (* (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))))))
215.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
185.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
170.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
151.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

2.7b
(log (exp (* (sin a) (sin b))))
0.2b
(/ (sin b) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b)))))))
0.2b
(* (sin a) (sin b))
0.2b
(* r (/ (sin b) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b))))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
16×associate-*r*
8×add-cbrt-cube add-exp-log
7×pow1
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod associate-/r* associate-*l* log-pow associate-/l*
2×*-commutative div-inv
1×cbrt-undiv exp-prod clear-num frac-2neg exp-to-pow div-exp rem-log-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod sin-mult
Calls
4 calls:
Slowest
4.0ms
(* (sin a) (sin b))
4.0ms
(/ (sin b) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b)))))))
3.0ms
(log (exp (* (sin a) (sin b))))
2.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b))))))))

series616.0ms

Calls
4 calls:
Slowest
329.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b))))))))
152.0ms
(/ (sin b) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b)))))))
74.0ms
(* (sin a) (sin b))
61.0ms
(log (exp (* (sin a) (sin b))))

simplify2.9s

Calls
66 calls:
Slowest
380.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b)))))) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b))))))) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b))))))))
199.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
174.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
142.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
123.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes289.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
4.4s2901×body1280valid
1.6s1866×body640valid
438.0ms773×body320valid
384.0ms2106×body80valid
159.0ms356×body160valid