Details

Time bar (total: 8.4m)

sample237.0ms

Algorithm
intervals
Results
91.0ms53×body1280valid
69.0ms38×body640valid
44.0ms177×body80valid
16.0ms19×body320valid
6.0ms10×body160valid

simplify105.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
105.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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)))

rewrite88.0ms

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
51.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms
(/ 1 (sin B))
10.0ms
(/ x (tan B))

series312.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
151.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
139.0ms
(/ x (tan B))
21.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
743.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ (cbrt x) (cbrt (tan B))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B)))))))
629.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (cos B) (/ x (sin B)))))
569.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
556.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
551.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 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)))

rewrite74.0ms

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
29.0ms
(/ (* x (cos B)) (sin B))
22.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
10.0ms
(/ 1 (sin B))
8.0ms
(* x (cos B))

series370.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
135.0ms
(/ (* x (cos B)) (sin B))
64.0ms
(* x (cos B))
21.0ms
(/ 1 (sin B))

simplify39.8s

Counts
274 → 220
Calls
274 calls:
Slowest
679.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ (* x (cos B)) (sin B)) 1)))
469.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
432.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
419.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
403.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 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)))

rewrite85.0ms

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
51.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms
(/ (* x (cos B)) (sin B))
10.0ms
(* x (cos B))
6.0ms
(/ 1 (sin B))

series377.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(/ (* x (cos B)) (sin B))
147.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
52.0ms
(* x (cos B))
25.0ms
(/ 1 (sin B))

simplify39.8s

Counts
274 → 220
Calls
274 calls:
Slowest
643.0ms
(fma (- (/ (cos B) (cbrt (sin B)))) (/ x (* (cbrt (sin B)) (cbrt (sin B)))) (* (/ (cos B) (cbrt (sin B))) (/ x (* (cbrt (sin B)) (cbrt (sin B))))))
483.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
400.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (cbrt (/ (* x (cos B)) (sin B))) (* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B)))))))
386.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))
384.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

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
26.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
21.0ms
(/ (cos B) (/ (sin B) x))
17.0ms
(/ 1 (sin B))
15.0ms
(/ (sin B) x)

series331.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
113.0ms
(/ (cos B) (/ (sin B) x))
52.0ms
(/ (sin B) x)
21.0ms
(/ 1 (sin B))

simplify5.4m

Counts
1340 → 762
Calls
1340 calls:
Slowest
950.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ (cos B) (/ (cbrt (sin B)) (sqrt x))) (/ 1 (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt x))))))
836.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ (sqrt (cos B)) (/ 1 x)) (/ (sqrt (cos B)) (sin B)))))
801.0ms
(fma (- (/ (cbrt (cos B)) (/ (sqrt (sin B)) (sqrt x)))) (/ (* (cbrt (cos B)) (cbrt (cos B))) (/ (sqrt (sin B)) (sqrt x))) (* (/ (cbrt (cos B)) (/ (sqrt (sin B)) (sqrt x))) (/ (* (cbrt (cos B)) (cbrt (cos B))) (/ (sqrt (sin B)) (sqrt x)))))
783.0ms
(fma (- (/ (sqrt (cos B)) (/ (sin B) (cbrt x)))) (/ (sqrt (cos B)) (/ 1 (* (cbrt x) (cbrt x)))) (* (/ (sqrt (cos B)) (/ (sin B) (cbrt x))) (/ (sqrt (cos B)) (/ 1 (* (cbrt x) (cbrt x))))))
718.0ms
(fma (- (/ (sqrt (cos B)) (/ (cbrt (sin B)) x))) (/ (sqrt (cos B)) (/ (* (cbrt (sin B)) (cbrt (sin B))) 1)) (* (/ (sqrt (cos B)) (/ (cbrt (sin B)) x)) (/ (sqrt (cos B)) (/ (* (cbrt (sin B)) (cbrt (sin B))) 1))))

prune9.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample9.7s

Algorithm
intervals
Results
3.8s1655×body1280valid
2.8s1395×body640valid
1.5s5018×body80valid
786.0ms679×body320valid
346.0ms404×body160valid