Details

Time bar (total: 2.3m)

sample885.0ms

Algorithm
intervals
Results
539.0ms158×body80valid
88.0ms44×body1280valid
81.0ms55×body640valid
23.0ms19×body320valid
10.0ms14×body160valid

simplify142.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
141.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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)))

rewrite68.0ms

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
39.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
13.0ms
(/ x (tan B))
9.0ms
(/ 1 (sin B))

series280.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
143.0ms
(/ x (tan B))
121.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
16.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
625.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
601.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
584.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
584.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
570.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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)))

rewrite464.0ms

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
430.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
14.0ms
(/ (* x (cos B)) (sin B))
8.0ms
(* x (cos B))
6.0ms
(/ 1 (sin B))

series346.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(/ (* x (cos B)) (sin B))
121.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
43.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify42.5s

Counts
274 → 220
Calls
274 calls:
Slowest
662.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))
498.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
446.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
419.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))
409.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (cbrt (/ (* x (cos B)) (sin B))) (* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B)))))))

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

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)))

rewrite30.0ms

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
20.0ms
(* (cbrt (cos B)) (cbrt (cos B)))
3.0ms
(cbrt (cos B))
2.0ms
(cbrt (cos B))
2.0ms
(cbrt (cos B))

series645.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
249.0ms
(* (cbrt (cos B)) (cbrt (cos B)))
149.0ms
(cbrt (cos B))
132.0ms
(cbrt (cos B))
114.0ms
(cbrt (cos B))

simplify1.6s

Counts
65 → 97
Calls
65 calls:
Slowest
512.0ms
(- 1 (+ (* 1/405 (pow B 6)) (* 1/3 (pow B 2))))
236.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
210.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
203.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
88.0ms
(* (* (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

localize46.0ms

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))

rewrite130.0ms

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
44.0ms
(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
42.0ms
(* (sin B) (* x (cos B)))
24.0ms
(* (sin B) (sin B))
17.0ms
(* x (cos B))

series326.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
105.0ms
(* (sin B) (* x (cos B)))
51.0ms
(* x (cos B))
21.0ms
(* (sin B) (sin B))

simplify4.7s

Counts
70 → 112
Calls
70 calls:
Slowest
500.0ms
(* (* (* (sin B) (sin B)) (sin B)) (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))))
459.0ms
(* (* (* (sin B) (sin B)) (sin B)) (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))))
453.0ms
(- (* (sin B) (sin B)) (* (* (sin B) (* x (cos B))) (* (sin B) (* x (cos B)))))
288.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
280.0ms
(- (+ (* 2/45 (pow B 6)) (pow B 2)) (* 1/3 (pow B 4)))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes129.0ms

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
3.2s1653×body1280valid
2.3s1413×body640valid
1.9s4982×body80valid
780.0ms762×body320valid
217.0ms342×body160valid