Details

Time bar (total: 4.1m)

sample959.0ms

Algorithm
intervals
Results
573.0ms79×body1280valid
203.0ms57×body2560valid
50.0ms60×body640valid
21.0ms34×body320valid
6.0ms15×body160valid
2.0ms11×body80valid

simplify50.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
49.0ms
(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize18.0ms

Local error

Found 3 expressions with local error:

1.9b
(- x (tan x))
1.9b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×fma-neg
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
3 → 113
Calls
3 calls:
Slowest
39.0ms
(/ (- x (sin x)) (- x (tan x)))
13.0ms
(- x (sin x))
12.0ms
(- x (tan x))

series270.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
124.0ms
(/ (- x (sin x)) (- x (tan x)))
101.0ms
(- x (tan x))
43.0ms
(- x (sin x))

simplify6.1s

Counts
122 → 122
Calls
122 calls:
Slowest
517.0ms
(- (+ 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)))))
498.0ms
(- (+ 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)))))
335.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
324.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
207.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

15.6b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.3b
(fma -27/2800 (* (* x x) (* x x)) -1/2)
0.1b
(* (* x x) (* x x))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
114×pow1
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus
15×add-cbrt-cube add-exp-log
13×pow2
8×prod-exp cbrt-unprod
3×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×swap-sqr associate-*r* associate-*l* *-commutative unswap-sqr
Counts
3 → 88
Calls
3 calls:
Slowest
34.0ms
(* (* x x) (* x x))
0.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)

series236.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
132.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
56.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
48.0ms
(* (* x x) (* x x))

simplify2.7s

Counts
76 → 97
Calls
76 calls:
Slowest
380.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
345.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
316.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
313.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
164.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune800.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

15.6b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.3b
(fma -27/2800 (* (* x x) (* x x)) -1/2)
0.1b
(* (* x x) (* x x))
0.0b
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
116×pow1
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus
16×add-cbrt-cube add-exp-log
13×pow2
8×prod-exp cbrt-unprod
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u log-prod log-pow insert-posit16 log1p-expm1-u add-log-exp
3×exp-prod fma-udef
1×swap-sqr rem-log-exp associate-*r* associate-*l* exp-sum *-commutative unswap-sqr
Counts
4 → 107
Calls
4 calls:
Slowest
46.0ms
(* (* x x) (* x x))
5.0ms
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
1.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)

series352.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
81.0ms
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
68.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
39.0ms
(* (* x x) (* x x))

simplify4.5s

Counts
87 → 119
Calls
87 calls:
Slowest
389.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
344.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
323.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
283.0ms
(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
282.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.9b
(- x (tan x))
1.9b
(- x (tan x))
1.9b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
703×add-sqr-sqrt
678×times-frac
459×prod-diff
417×add-cube-cbrt
147×distribute-lft-out--
141×difference-of-squares
92×associate-/r/
49×flip3-- flip--
46×div-inv
27×fma-neg
10×add-log-exp
6×add-cbrt-cube add-exp-log
5×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×sub-neg distribute-rgt-out-- diff-log associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp frac-sub sub-div
Counts
4 → 592
Calls
4 calls:
Slowest
71.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
27.0ms
(/ (sin x) (- x (tan x)))
6.0ms
(- x (tan x))
5.0ms
(- x (tan x))

series497.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
273.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
83.0ms
(- x (tan x))
80.0ms
(- x (tan x))
61.0ms
(/ (sin x) (- x (tan x)))

simplify3.4m

Counts
1036 → 604
Calls
1036 calls:
Slowest
699.0ms
(fma (sqrt (/ x (- x (tan x)))) (sqrt (/ x (- x (tan x)))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
660.0ms
(fma (/ (sqrt x) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ (sqrt x) (cbrt (- x (tan x)))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
652.0ms
(fma (/ (sqrt x) (+ (sqrt x) (sqrt (tan x)))) (/ (sqrt x) (- (sqrt x) (sqrt (tan x)))) (- (* (/ (sqrt (sin x)) (- (sqrt x) (sqrt (tan x)))) (/ (sqrt (sin x)) (+ (sqrt x) (sqrt (tan x)))))))
636.0ms
(fma (- (/ (cbrt (sin x)) (- (sqrt x) (sqrt (tan x))))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (+ (sqrt x) (sqrt (tan x)))) (* (/ (cbrt (sin x)) (- (sqrt x) (sqrt (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (+ (sqrt x) (sqrt (tan x))))))
622.0ms
(fma (- (/ (sqrt (sin x)) (- (sqrt x) (sqrt (tan x))))) (/ (sqrt (sin x)) (+ (sqrt x) (sqrt (tan x)))) (* (/ (sqrt (sin x)) (- (sqrt x) (sqrt (tan x)))) (/ (sqrt (sin x)) (+ (sqrt x) (sqrt (tan x))))))

prune5.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.6b

bsearch173.0ms

end0.0ms

sample17.1s

Algorithm
intervals
Results
7.0s1629×body2560valid
5.8s2763×body1280valid
2.4s1801×body640valid
1.0s985×body320valid
642.0ms488×body160valid
83.0ms334×body80valid