Details

Time bar (total: 24.4s)

sample666.0ms

Algorithm
intervals
Results
95.0ms31×body640valid
70.0ms37×body1280valid
37.0ms146×body80valid
34.0ms30×body320valid
7.0ms12×body160valid

simplify104.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.1b
(- 1 (* (tan x) (tan x)))
0.1b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

rewrite54.0ms

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
16.0ms
(* (tan x) (tan x))
15.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
14.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (* (tan x) (tan x)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
79.0ms
(* (tan x) (tan x))
66.0ms
(- 1 (* (tan x) (tan x)))
61.0ms
(* (tan x) (tan x))

simplify1.4s

Counts
140 → 140

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.2b
(/ (* (sin x) (tan x)) (cos x))
0.1b
(- 1 (/ (* (sin x) (tan x)) (cos x)))
0.1b
(* (sin x) (tan x))

rewrite69.0ms

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 prod-exp associate-*r/ 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-*l/ pow-sqr pow-prod-up flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 120
Calls
4 calls:
Slowest
27.0ms
(/ (* (sin x) (tan x)) (cos x))
18.0ms
(* (tan x) (tan x))
11.0ms
(* (sin x) (tan x))
11.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))
82.0ms
(* (sin x) (tan x))
71.0ms
(/ (* (sin x) (tan x)) (cos x))
46.0ms
(* (tan x) (tan x))

simplify2.7s

Counts
132 → 132

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

29.9b
(fma (- (/ 1 (cos x))) (* (sin x) (tan x)) (* (/ 1 (cos x)) (* (sin x) (tan x))))
0.3b
(* (tan x) (tan x))
0.2b
(* (/ 1 (cos x)) (* (sin x) (tan x)))
0.2b
(* (/ 1 (cos x)) (* (sin x) (tan x)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
30×add-cbrt-cube
29×associate-*l*
25×prod-exp
24×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
21×pow1
18×times-frac
13×cbrt-unprod
8×div-exp tan-quot
7×pow-prod-down associate-*r/
5×associate-*r*
4×expm1-log1p-u cbrt-undiv rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×frac-times swap-sqr associate-*l/ *-commutative
2×div-inv
1×pow2 pow-plus pow-sqr pow-prod-up fma-udef unswap-sqr
Counts
4 → 126
Calls
4 calls:
Slowest
37.0ms
(* (/ 1 (cos x)) (* (sin x) (tan x)))
34.0ms
(* (/ 1 (cos x)) (* (sin x) (tan x)))
13.0ms
(* (tan x) (tan x))
0.0ms
(fma (- (/ 1 (cos x))) (* (sin x) (tan x)) (* (/ 1 (cos x)) (* (sin x) (tan x))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
190.0ms
(fma (- (/ 1 (cos x))) (* (sin x) (tan x)) (* (/ 1 (cos x)) (* (sin x) (tan x))))
89.0ms
(* (/ 1 (cos x)) (* (sin x) (tan x)))
75.0ms
(* (/ 1 (cos x)) (* (sin x) (tan x)))
47.0ms
(* (tan x) (tan x))

simplify1.5s

Counts
138 → 138

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

29.9b
(fma (- (/ 1 (cos x))) (* (sin x) (tan x)) (* (/ 1 (cos x)) (* (sin x) (tan x))))
0.2b
(* (cos x) (cos x))
0.2b
(* (sin x) (sin x))
0.2b
(* (/ 1 (cos x)) (* (sin x) (tan x)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
23×add-sqr-sqrt pow1
20×add-cbrt-cube
19×*-un-lft-identity associate-*l* add-cube-cbrt
14×prod-exp
9×times-frac
8×cbrt-unprod
7×associate-*r*
6×swap-sqr
5×pow-prod-down
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/ *-commutative
2×pow2 cbrt-undiv rec-exp pow-plus 1-exp tan-quot pow-sqr pow-prod-up unswap-sqr
1×frac-times sqr-cos associate-*l/ cos-mult fma-udef sqr-sin div-inv sin-mult
Counts
4 → 113
Calls
4 calls:
Slowest
57.0ms
(* (/ 1 (cos x)) (* (sin x) (tan x)))
13.0ms
(* (sin x) (sin x))
9.0ms
(* (cos x) (cos x))
0.0ms
(fma (- (/ 1 (cos x))) (* (sin x) (tan x)) (* (/ 1 (cos x)) (* (sin x) (tan x))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(fma (- (/ 1 (cos x))) (* (sin x) (tan x)) (* (/ 1 (cos x)) (* (sin x) (tan x))))
84.0ms
(* (/ 1 (cos x)) (* (sin x) (tan x)))
35.0ms
(* (sin x) (sin x))
18.0ms
(* (cos x) (cos x))

simplify2.8s

Counts
125 → 125

prune2.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes348.0ms

Accuracy

0% (0.3b remaining)

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

bsearch13.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.7s1574×body1280valid
1.8s1198×body640valid
758.0ms4268×body80valid
454.0ms640×body320valid
172.0ms320×body160valid