Details

Time bar (total: 2.2m)

sample252.0ms

Algorithm
intervals
Results
97.0ms44×body1280valid
71.0ms55×body640valid
43.0ms158×body80valid
17.0ms19×body320valid
8.0ms14×body160valid

simplify126.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
126.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

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
36.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms
(/ 1 (sin B))
10.0ms
(/ x (tan B))

series338.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
155.0ms
(/ x (tan B))
155.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
28.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
913.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
635.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
611.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
572.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
550.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
107×add-sqr-sqrt
105×*-un-lft-identity
98×add-cube-cbrt
91×prod-diff
28×div-inv
15×add-exp-log
13×add-cbrt-cube fma-neg
7×pow1
6×associate-/r* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u associate-/l*
3×cbrt-undiv distribute-rgt-out-- associate-*r* associate-*l* difference-of-squares
2×clear-num frac-2neg prod-exp cbrt-unprod distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div unswap-sqr
Counts
4 → 208
Calls
4 calls:
Slowest
49.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms
(/ (* x (cos B)) (sin B))
7.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series349.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(/ (* x (cos B)) (sin B))
125.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
65.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify39.8s

Counts
274 → 220
Calls
274 calls:
Slowest
600.0ms
(fma (- (/ (* x (cos B)) (sin B))) 1 (* (/ (* x (cos B)) (sin B)) 1))
429.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
416.0ms
(fma (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))) (/ 1 (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
400.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))
381.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos B))
0.3b
(cbrt (cos B))
0.3b
(cbrt (cos B))
0.2b
(* (cbrt (cos B)) (cbrt (cos B)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
14.0ms
(* (cbrt (cos B)) (cbrt (cos B)))
1.0ms
(cbrt (cos B))
1.0ms
(cbrt (cos B))
1.0ms
(cbrt (cos B))

series678.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
242.0ms
(* (cbrt (cos B)) (cbrt (cos B)))
153.0ms
(cbrt (cos B))
144.0ms
(cbrt (cos B))
140.0ms
(cbrt (cos B))

simplify1.6s

Counts
65 → 97
Calls
65 calls:
Slowest
452.0ms
(- 1 (+ (* 1/405 (pow B 6)) (* 1/3 (pow B 2))))
251.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
227.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
190.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
87.0ms
(* (* (cbrt (cbrt (cos B))) (cbrt (cbrt (cos B)))) (* (cbrt (cbrt (cos B))) (cbrt (cbrt (cos B)))))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

10.8b
(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
0.3b
(* (sin B) (sin B))
0.2b
(* (sin B) (* x (cos B)))
0.1b
(* x (cos B))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
9×associate-*l*
7×associate-*r*
6×prod-exp cbrt-unprod
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×times-frac swap-sqr *-commutative associate-/l*
2×cbrt-undiv div-exp sin-mult unswap-sqr associate-/l/
1×pow2 clear-num associate-/r* frac-2neg pow-plus flip3-- div-sub associate-/r/ pow-sqr pow-prod-up sqr-sin div-inv flip--
Counts
4 → 100
Calls
4 calls:
Slowest
43.0ms
(* (sin B) (* x (cos B)))
31.0ms
(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
22.0ms
(* (sin B) (sin B))
15.0ms
(* x (cos B))

series359.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
98.0ms
(* (sin B) (* x (cos B)))
65.0ms
(* x (cos B))
31.0ms
(* (sin B) (sin B))

simplify5.0s

Counts
70 → 112
Calls
70 calls:
Slowest
840.0ms
(- (* (sin B) (sin B)) (* (* (sin B) (* x (cos B))) (* (sin B) (* x (cos B)))))
513.0ms
(* (* (* (sin B) (sin B)) (sin B)) (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))))
459.0ms
(* (* (* (sin B) (sin B)) (sin B)) (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))))
343.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
264.0ms
(/ (- (sin B) (* (sin B) (* x (cos B)))) (sin B))

prune926.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.4s1653×body1280valid
2.2s4982×body80valid
1.9s1413×body640valid
731.0ms762×body320valid
193.0ms342×body160valid