Details

Time bar (total: 2.2m)

sample974.0ms

Algorithm
intervals
Results
278.0ms37×body2560valid
250.0ms100×body1280valid
95.0ms60×body640valid
23.0ms31×body320valid
9.0ms18×body160valid
7.0ms10×body80valid

simplify30.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
30.0ms
(/ (- x (sin x)) (- x (tan x)))

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize20.0ms

Local error

Found 3 expressions with local error:

2.1b
(- x (tan x))
2.1b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt *-un-lft-identity
25×times-frac
15×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×pow1 insert-posit16
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
3 → 83
Calls
3 calls:
Slowest
19.0ms
(/ (- x (sin x)) (- x (tan x)))
6.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series199.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
86.0ms
(/ (- x (sin x)) (- x (tan x)))
76.0ms
(- x (tan x))
36.0ms
(- x (sin x))

simplify3.1s

Counts
82 → 92
Calls
82 calls:
Slowest
433.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
396.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
257.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
236.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
232.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))

prune769.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

12.3b
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
0.4b
(* (* x x) 9/40)
0.1b
(* (* x x) (* x x))
0.1b
(* (* (* x x) (* x x)) 27/2800)

rewrite330.0ms

Algorithm
rewrite-expression-head
Rules
138×pow1
39×add-cbrt-cube pow-prod-down add-exp-log
36×pow-prod-up
24×prod-exp cbrt-unprod
22×pow-sqr
18×pow-plus
13×pow2
9×add-log-exp
8×add-sqr-sqrt
7×associate-*r*
6×*-un-lft-identity add-cube-cbrt
4×insert-posit16
3×associate-*l* *-commutative unswap-sqr
2×diff-log
1×sum-log sub-neg flip3-- swap-sqr flip-- associate--r+
Counts
4 → 128
Calls
4 calls:
Slowest
142.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
129.0ms
(* (* (* x x) (* x x)) 27/2800)
39.0ms
(* (* x x) (* x x))
15.0ms
(* (* x x) 9/40)

series226.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
76.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
55.0ms
(* (* x x) (* x x))
55.0ms
(* (* (* x x) (* x x)) 27/2800)
40.0ms
(* (* x x) 9/40)

simplify6.9s

Counts
111 → 140
Calls
111 calls:
Slowest
513.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
486.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
464.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
416.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
399.0ms
(* (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))) (* (* 27/2800 27/2800) 27/2800))

prune965.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
2.1b
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
0.2b
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
0.1b
(/ (/ (sin x) (cos x)) x)

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
372×times-frac
245×add-sqr-sqrt
196×*-un-lft-identity
188×add-cube-cbrt
45×add-cbrt-cube add-exp-log
43×swap-sqr associate-*r* associate-*l*
23×div-inv
21×cbrt-undiv div-exp
13×associate-/l*
11×pow1
9×prod-exp cbrt-unprod unswap-sqr
8×add-log-exp
6×difference-of-squares
4×insert-posit16 distribute-lft-out--
3×associate-/r*
1×pow2 frac-times +-commutative clear-num sum-log sub-neg frac-2neg flip3-+ pow-plus flip3-- distribute-rgt-out-- diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up frac-sub flip-+ flip-- sub-div associate-/l/
Counts
4 → 282
Calls
4 calls:
Slowest
36.0ms
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
28.0ms
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
18.0ms
(/ (/ (sin x) (cos x)) x)
14.0ms
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(- (/ (/ (sin x) (cos x)) x) (/ (sin x) x))
111.0ms
(+ (* (/ (sin x) x) (/ (/ (sin x) (cos x)) x)) -1)
98.0ms
(* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))
61.0ms
(/ (/ (sin x) (cos x)) x)

simplify35.3s

Counts
351 → 294
Calls
351 calls:
Slowest
810.0ms
(* (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (sqrt x)) (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (sqrt x)))
792.0ms
(* (* (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (/ (/ (sin x) (cos x)) x)) (/ (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* x x) x)))
749.0ms
(/ (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* x x) x))
718.0ms
(* (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt (cos x))) (* (cbrt x) (cbrt x))) (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt (cos x))) (* (cbrt x) (cbrt x))))
712.0ms
(* (/ (/ 1 (* (cbrt (cos x)) (cbrt (cos x)))) (sqrt x)) (/ (/ 1 (* (cbrt (cos x)) (cbrt (cos x)))) (sqrt x)))

prune3.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

30.9b
(/ (- (pow x 3) (pow (tan x) 3)) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))
2.1b
(- x (sin x))
2.1b
(- (pow x 3) (pow (tan x) 3))
0.3b
(pow (tan x) 3)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
159×add-sqr-sqrt
89×*-un-lft-identity
81×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
26×distribute-lft-out--
25×associate-/l*
8×add-log-exp
7×add-cbrt-cube add-exp-log
5×pow1 difference-cubes
4×insert-posit16
3×pow-unpow associate-/r* flip3-- flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×cube-div cube-mult pow-to-exp cbrt-undiv clear-num pow-pow frac-2neg flip3-+ unpow3 div-sub div-exp pow-exp tan-quot flip-+ div-inv rem-cube-cbrt
Counts
4 → 196
Calls
4 calls:
Slowest
77.0ms
(/ (- (pow x 3) (pow (tan x) 3)) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))
11.0ms
(- (pow x 3) (pow (tan x) 3))
5.0ms
(- x (sin x))
3.0ms
(pow (tan x) 3)

series649.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
339.0ms
(/ (- (pow x 3) (pow (tan x) 3)) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))
191.0ms
(- (pow x 3) (pow (tan x) 3))
65.0ms
(- x (sin x))
54.0ms
(pow (tan x) 3)

simplify57.7s

Counts
255 → 208
Calls
255 calls:
Slowest
733.0ms
(/ (+ (sqrt (pow x 3)) (sqrt (pow (tan x) 3))) 1)
685.0ms
(/ (* (cbrt (- (pow x 3) (pow (tan x) 3))) (cbrt (- (pow x 3) (pow (tan x) 3)))) (sqrt (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x))))))
489.0ms
(/ (* (* (- (pow x 3) (pow (tan x) 3)) (- (pow x 3) (pow (tan x) 3))) (- (pow x 3) (pow (tan x) 3))) (* (* (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x))))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x))))))
487.0ms
(/ (- (pow (sqrt x) 3) (pow (sqrt (tan x)) 3)) (cbrt (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x))))))
485.0ms
(/ (+ (pow (sqrt x) 3) (pow (sqrt (tan x)) 3)) (* (cbrt (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x))))) (cbrt (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))))

prune2.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.6b

bsearch203.0ms

end0.0ms

sample16.9s

Algorithm
intervals
Results
6.7s1544×body2560valid
6.4s2768×body1280valid
2.6s1887×body640valid
726.0ms944×body320valid
280.0ms497×body160valid
104.0ms360×body80valid