Details

Time bar (total: 4.1m)

sample533.0ms

Algorithm
intervals
Results
172.0ms43×body2560valid
147.0ms104×body1280valid
103.0ms61×body640valid
12.0ms21×body320valid
6.0ms17×body160valid
2.0ms10×body80valid

simplify45.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
44.0ms
(/ (- x (sin x)) (- x (tan x)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize53.0ms

Local error

Found 3 expressions with local error:

1.2b
(- x (sin x))
1.1b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite37.0ms

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
19.0ms
(/ (- x (sin x)) (- x (tan x)))
8.0ms
(- x (sin x))
5.0ms
(- x (tan x))

series266.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
130.0ms
(/ (- x (sin x)) (- x (tan x)))
69.0ms
(- x (tan x))
67.0ms
(- x (sin x))

simplify5.8s

Counts
122 → 122
Calls
122 calls:
Slowest
528.0ms
(- (+ 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)))))
458.0ms
(- (+ 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)))))
362.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
281.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
207.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

15.3b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.2b
(* (* x x) (* x x))
0.0b
(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite43.0ms

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
39.0ms
(* (* x x) (* x x))
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)

series219.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
120.0ms
(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))
42.0ms
(* (* x x) (* x x))

simplify2.8s

Counts
76 → 97
Calls
76 calls:
Slowest
383.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
341.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
340.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
320.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
197.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune808.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

15.3b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.5b
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
0.2b
(* (* x x) (* x x))
0.0b
(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite30.0ms

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
24.0ms
(* (* x x) (* x x))
3.0ms
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
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)

series290.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
67.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
63.0ms
(log (exp (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
44.0ms
(* (* x x) (* x x))

simplify4.4s

Counts
87 → 119
Calls
87 calls:
Slowest
436.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
422.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
301.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
284.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
256.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.1b
(- x (tan x))
1.1b
(- 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
84.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
22.0ms
(/ (sin x) (- x (tan x)))
10.0ms
(- x (tan x))
10.0ms
(- x (tan x))

series504.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
291.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
85.0ms
(/ (sin x) (- x (tan x)))
65.0ms
(- x (tan x))
63.0ms
(- x (tan x))

simplify3.4m

Counts
1036 → 604
Calls
1036 calls:
Slowest
711.0ms
(fma (/ 1 (sqrt (- x (tan x)))) (/ x (sqrt (- x (tan x)))) (- (* (/ (sin x) (sqrt (- x (tan x)))) (/ 1 (sqrt (- x (tan x)))))))
675.0ms
(fma (/ x (- (* x x) (* (tan x) (tan x)))) (+ x (tan x)) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
663.0ms
(fma 1 (/ x (- x (tan x))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
658.0ms
(fma (- (/ (cbrt (sin x)) (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1)))
645.0ms
(fma (/ (sqrt x) (sqrt (- x (tan x)))) (/ (sqrt x) (sqrt (- x (tan x)))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))

prune5.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch151.0ms

end0.0ms

sample17.4s

Algorithm
intervals
Results
7.6s1640×body2560valid
5.0s2729×body1280valid
3.0s1904×body640valid
758.0ms489×body160valid
680.0ms852×body320valid
101.0ms386×body80valid