Details

Time bar (total: 1.3m)

sample238.0ms

Algorithm
intervals
Results
92.0ms50×body1280valid
32.0ms41×body640valid
21.0ms136×body80valid
15.0ms22×body320valid
3.0ms7×body160valid

simplify92.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
92.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.2b
(- 1 (* (tan x) (tan x)))
0.2b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
24×add-cube-cbrt
18×pow1
15×times-frac
10×add-cbrt-cube add-exp-log difference-of-squares
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg prod-diff
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
4 → 128
Calls
4 calls:
Slowest
24.0ms
(* (tan x) (tan x))
21.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
20.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (* (tan x) (tan x)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
60.0ms
(- 1 (* (tan x) (tan x)))
49.0ms
(* (tan x) (tan x))
46.0ms
(* (tan x) (tan x))

simplify5.9s

Counts
119 → 140
Calls
119 calls:
Slowest
565.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
443.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
347.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
344.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
315.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
0.2b
(+ (tan x) 1)
0.2b
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
0.2b
(- 1 (tan x))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
62×*-un-lft-identity
37×times-frac
34×add-cube-cbrt
22×associate-*r*
16×difference-of-squares
11×add-cbrt-cube add-exp-log
9×prod-diff
8×distribute-lft-out-- add-log-exp
6×pow1 associate-/l*
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×associate-/r* fma-def flip3-+ fma-neg flip-+
2×frac-times cbrt-undiv flip3-- div-exp associate-*l/ prod-exp cbrt-unprod div-inv flip-- distribute-lft-out unswap-sqr associate-/l/
1×+-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub pow-prod-down associate-*r/ *-commutative
Counts
4 → 142
Calls
4 calls:
Slowest
56.0ms
(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
12.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
6.0ms
(- 1 (tan x))
6.0ms
(+ (tan x) 1)

series290.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
85.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
25.0ms
(+ (tan x) 1)
24.0ms
(- 1 (tan x))

simplify9.0s

Counts
130 → 154
Calls
130 calls:
Slowest
758.0ms
(* (+ (* (tan x) (tan x)) (- (* 1 1) (* (tan x) 1))) (fma (tan x) (tan x) 1))
618.0ms
(* (- (* (tan x) (tan x)) (* 1 1)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
479.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
354.0ms
(/ (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))) (* (* (fma (tan x) (tan x) 1) (fma (tan x) (tan x) 1)) (fma (tan x) (tan x) 1)))
331.0ms
(- 1 (+ x (* 1/3 (pow x 3))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.2b
(/ (* (tan x) (sin x)) (cos x))
0.2b
(- 1 (/ (* (tan x) (sin x)) (cos x)))
0.2b
(* (tan x) (sin x))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
26×add-cube-cbrt
21×prod-diff
13×pow1 add-cbrt-cube add-exp-log
12×times-frac
6×associate-*r* associate-*l* tan-quot add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×associate-/r* fma-neg swap-sqr associate-*l/ prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative difference-of-squares unswap-sqr
1×pow2 frac-times clear-num sub-neg frac-2neg pow-plus flip3-- diff-log associate-*r/ pow-sqr pow-prod-up flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 120
Calls
4 calls:
Slowest
31.0ms
(/ (* (tan x) (sin x)) (cos x))
28.0ms
(* (tan x) (tan x))
25.0ms
(* (tan x) (sin x))
25.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(/ (* (tan x) (sin x)) (cos x))
84.0ms
(* (tan x) (sin x))
61.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))
33.0ms
(* (tan x) (tan x))

simplify10.9s

Counts
113 → 132
Calls
113 calls:
Slowest
323.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
311.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
306.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (/ 1 (cos x)) (* (tan x) (sin x)))))
294.0ms
(fma 1 1 (- (* (/ 1 (cos x)) (* (tan x) (sin x)))))
293.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

13.0b
(sqrt (/ (* (tan x) (sin x)) (cos x)))
13.0b
(sqrt (/ (* (tan x) (sin x)) (cos x)))
0.3b
(- 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))
0.2b
(* (+ 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))) (- 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
90×prod-diff
87×add-sqr-sqrt
84×sqrt-prod
81×*-un-lft-identity
68×add-cube-cbrt
33×times-frac
32×distribute-rgt-in distribute-lft-in
11×div-inv
9×associate-*r*
8×pow1 difference-of-squares
6×add-cbrt-cube add-exp-log add-log-exp
5×associate-*l*
4×expm1-log1p-u frac-times flip3-- insert-posit16 log1p-expm1-u flip-- distribute-lft-out--
3×sub-neg flip3-+ fma-neg flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div associate-*l/ associate-*r/ distribute-lft-out
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 197
Calls
4 calls:
Slowest
103.0ms
(* (+ 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))) (- 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))))
21.0ms
(- 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))
7.0ms
(sqrt (/ (* (tan x) (sin x)) (cos x)))
4.0ms
(sqrt (/ (* (tan x) (sin x)) (cos x)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
243.0ms
(* (+ 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))) (- 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))))
104.0ms
(sqrt (/ (* (tan x) (sin x)) (cos x)))
101.0ms
(sqrt (/ (* (tan x) (sin x)) (cos x)))
96.0ms
(- 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))

simplify36.2s

Counts
199 → 209
Calls
199 calls:
Slowest
1.1s
(* (* (* (+ 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))) (+ 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))) (+ 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))) (* (* (- 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))) (- 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))) (- 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))))
1.1s
(* (+ (* 1 1) (- (* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x)))) (* 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))))) (+ (* 1 1) (+ (* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x)))) (* 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))))))
1.0s
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
947.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
793.0ms
(* (fma (- (cbrt (sqrt (/ (* (tan x) (sin x)) (cos x))))) (* (cbrt (sqrt (/ (* (tan x) (sin x)) (cos x)))) (cbrt (sqrt (/ (* (tan x) (sin x)) (cos x))))) (* (cbrt (sqrt (/ (* (tan x) (sin x)) (cos x)))) (* (cbrt (sqrt (/ (* (tan x) (sin x)) (cos x)))) (cbrt (sqrt (/ (* (tan x) (sin x)) (cos x))))))) (+ 1 (sqrt (/ (* (tan x) (sin x)) (cos x)))))

prune2.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes301.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.3s1522×body1280valid
1.7s1249×body640valid
827.0ms4325×body80valid
593.0ms300×body160valid
498.0ms604×body320valid