Details

Time bar (total: 6.9m)

sample582.0ms

Algorithm
intervals
Results
319.0ms49×body1280valid
103.0ms178×body80valid
60.0ms40×body640valid
22.0ms19×body320valid
8.0ms11×body160valid

simplify132.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
131.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ x (tan B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ x (tan B)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
232×add-sqr-sqrt
224×*-un-lft-identity
215×add-cube-cbrt
182×prod-diff
31×div-inv
14×tan-quot associate-/r/
13×fma-neg
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u distribute-lft-out--
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
3 → 285
Calls
3 calls:
Slowest
26.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms
(/ x (tan B))
5.0ms
(/ 1 (sin B))

series438.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
281.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
138.0ms
(/ x (tan B))
18.0ms
(/ 1 (sin B))

simplify1.1m

Counts
456 → 294
Calls
456 calls:
Slowest
711.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ (cbrt x) (sqrt (tan B))) (/ (* (cbrt x) (cbrt x)) (sqrt (tan B))))))
667.0ms
(fma (- (/ (cbrt x) (cbrt (tan B)))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ (cbrt x) (cbrt (tan B))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B))))))
631.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
572.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
568.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ x (sin B)) (cos B))
0.1b
(/ 1 (sin B))
0.1b
(/ x (sin B))
0.0b
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
46×times-frac
42×*-un-lft-identity add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube fma-neg associate-*l* prod-diff
7×pow1
6×associate-/r* associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-*r* associate-*l/
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div
Counts
4 → 142
Calls
4 calls:
Slowest
47.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
14.0ms
(* (/ x (sin B)) (cos B))
9.0ms
(/ 1 (sin B))
7.0ms
(/ x (sin B))

series379.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
125.0ms
(* (/ x (sin B)) (cos B))
71.0ms
(/ x (sin B))
18.0ms
(/ 1 (sin B))

simplify5.5s

Counts
130 → 154
Calls
130 calls:
Slowest
391.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
244.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
224.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
214.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
207.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (cos B) (/ x (sin B)))))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos B) (/ (sin B) x))
0.1b
(/ (sin B) x)
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
1373×times-frac
862×add-sqr-sqrt
842×*-un-lft-identity
832×add-cube-cbrt
572×prod-diff
105×div-inv
19×associate-/r*
15×add-exp-log
14×associate-/r/
13×add-cbrt-cube fma-neg
9×associate-/l* difference-of-squares
6×div-exp add-log-exp
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×clear-num frac-2neg distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
4 → 750
Calls
4 calls:
Slowest
55.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
10.0ms
(/ (cos B) (/ (sin B) x))
10.0ms
(/ (sin B) x)
10.0ms
(/ 1 (sin B))

series287.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
104.0ms
(/ (cos B) (/ (sin B) x))
35.0ms
(/ (sin B) x)
30.0ms
(/ 1 (sin B))

simplify5.2m

Counts
1340 → 762
Calls
1340 calls:
Slowest
933.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ (sqrt (cos B)) (/ (cbrt (sin B)) (sqrt x))) (/ (sqrt (cos B)) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt x))))))
891.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ (cos B) (cbrt (/ (sin B) x))) (/ 1 (* (cbrt (/ (sin B) x)) (cbrt (/ (sin B) x)))))))
876.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ (cbrt (cos B)) (/ (sqrt (sin B)) (sqrt x))) (/ (* (cbrt (cos B)) (cbrt (cos B))) (/ (sqrt (sin B)) (sqrt x))))))
754.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ (cos B) (/ (sqrt (sin B)) (cbrt x))) (/ 1 (/ (sqrt (sin B)) (* (cbrt x) (cbrt x)))))))
746.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ 1 (/ (sin B) x)) (cos B))))

prune9.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1 (* x (cos B))) (sin B))
0.1b
(* x (cos B))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv flip-- unswap-sqr
Counts
2 → 54
Calls
2 calls:
Slowest
25.0ms
(/ (- 1 (* x (cos B))) (sin B))
11.0ms
(* x (cos B))

series140.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
95.0ms
(/ (- 1 (* x (cos B))) (sin B))
45.0ms
(* x (cos B))

simplify2.3s

Counts
44 → 60
Calls
44 calls:
Slowest
330.0ms
(/ (* (cbrt (- 1 (* x (cos B)))) (cbrt (- 1 (* x (cos B))))) (* (cbrt (sin B)) (cbrt (sin B))))
319.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
312.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
190.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
112.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune567.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.7s1765×body1280valid
2.4s1409×body640valid
1.5s4998×body80valid
589.0ms686×body320valid
200.0ms327×body160valid