Details

Time bar (total: 1.1m)

sample187.0ms

Algorithm
intervals
Results
40.0ms44×body1280valid
29.0ms45×body640valid
18.0ms134×body80valid
9.0ms21×body320valid
4.0ms12×body160valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
139.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

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
29.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
18.0ms
(* (tan x) (tan x))
16.0ms
(* (tan x) (tan x))
6.0ms
(- 1 (* (tan x) (tan x)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
87.0ms
(* (tan x) (tan x))
57.0ms
(* (tan x) (tan x))
44.0ms
(- 1 (* (tan x) (tan x)))

simplify11.4s

Counts
170 → 140
Calls
170 calls:
Slowest
739.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
595.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
592.0ms
(* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x))))
546.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
503.0ms
(* (* (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))) (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
19×*-un-lft-identity add-cube-cbrt
12×times-frac
11×pow1
8×add-cbrt-cube add-exp-log
6×add-log-exp
5×difference-of-squares
4×expm1-log1p-u associate-/r* tan-quot insert-posit16 log1p-expm1-u
3×fma-neg swap-sqr associate-*r* associate-*l* prod-diff associate-/l*
2×flip3-- associate-/r/ flip--
1×pow2 frac-times cbrt-undiv clear-num sub-neg frac-2neg pow-plus diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef div-inv unswap-sqr
Counts
4 → 100
Calls
4 calls:
Slowest
29.0ms
(* (tan x) (tan x))
8.0ms
(/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))
5.0ms
(- -1 (* (tan x) (tan x)))
1.0ms
(fma (tan x) (tan x) -1)

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))
70.0ms
(fma (tan x) (tan x) -1)
36.0ms
(- -1 (* (tan x) (tan x)))
34.0ms
(* (tan x) (tan x))

simplify11.7s

Counts
134 → 112
Calls
134 calls:
Slowest
916.0ms
(* (* (- -1 (* (tan x) (tan x))) (- -1 (* (tan x) (tan x)))) (- -1 (* (tan x) (tan x))))
540.0ms
(+ (* -1 -1) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* -1 (* (tan x) (tan x)))))
536.0ms
(/ (* (* (fma (tan x) (tan x) -1) (fma (tan x) (tan x) -1)) (fma (tan x) (tan x) -1)) (* (* (- -1 (* (tan x) (tan x))) (- -1 (* (tan x) (tan x)))) (- -1 (* (tan x) (tan x)))))
459.0ms
(- (pow -1 3) (pow (* (tan x) (tan x)) 3))
399.0ms
(- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×pow1
16×times-frac
10×add-cbrt-cube add-exp-log
8×tan-quot
6×difference-of-sqr--1 swap-sqr associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u associate-/l*
2×pow2 frac-times flip3-+ pow-plus 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 +-commutative clear-num sum-log fma-def frac-2neg flip3-- div-exp div-inv flip--
Counts
4 → 121
Calls
4 calls:
Slowest
47.0ms
(/ (+ (* (tan x) (tan x)) -1) (- -1 (* (tan x) (tan x))))
30.0ms
(* (tan x) (tan x))
20.0ms
(+ (* (tan x) (tan x)) -1)
17.0ms
(* (tan x) (tan x))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(/ (+ (* (tan x) (tan x)) -1) (- -1 (* (tan x) (tan x))))
58.0ms
(* (tan x) (tan x))
54.0ms
(+ (* (tan x) (tan x)) -1)
54.0ms
(* (tan x) (tan x))

simplify17.4s

Counts
157 → 133
Calls
157 calls:
Slowest
1.1s
(/ (+ (* (tan x) (tan x)) -1) (- (* -1 -1) (* (* (tan x) (tan x)) (* (tan x) (tan x)))))
553.0ms
(* (* (/ (+ (* (tan x) (tan x)) -1) (- -1 (* (tan x) (tan x)))) (/ (+ (* (tan x) (tan x)) -1) (- -1 (* (tan x) (tan x))))) (/ (+ (* (tan x) (tan x)) -1) (- -1 (* (tan x) (tan x)))))
516.0ms
(+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (- (* -1 -1) (* (* (tan x) (tan x)) -1)))
496.0ms
(* (- -1 (* (tan x) (tan x))) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (- (* -1 -1) (* (* (tan x) (tan x)) -1))))
437.0ms
(* (- -1 (* (tan x) (tan x))) (- (* (tan x) (tan x)) -1))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (tan x) (tan x) -1)
0.3b
(log (exp (/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))))
0.3b
(* (tan x) (tan x))
0.1b
(/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
26×*-un-lft-identity add-cube-cbrt
24×times-frac
19×log-pow
18×exp-prod
12×pow1
8×add-cbrt-cube add-exp-log
7×difference-of-squares
4×expm1-log1p-u associate-/r* tan-quot associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×log-prod swap-sqr associate-*r* associate-*l* associate-/l*
2×flip3-- div-inv flip--
1×pow2 frac-times cbrt-undiv clear-num frac-2neg pow-plus div-exp rem-log-exp pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef unswap-sqr
Counts
4 → 111
Calls
4 calls:
Slowest
29.0ms
(* (tan x) (tan x))
23.0ms
(log (exp (/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))))
14.0ms
(/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))
1.0ms
(fma (tan x) (tan x) -1)

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(log (exp (/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))))
142.0ms
(/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))
74.0ms
(fma (tan x) (tan x) -1)
56.0ms
(* (tan x) (tan x))

simplify13.0s

Counts
141 → 123
Calls
141 calls:
Slowest
702.0ms
(* (* (log (exp (/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x)))))) (log (exp (/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))))) (log (exp (/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x)))))))
596.0ms
(/ (* (* (fma (tan x) (tan x) -1) (fma (tan x) (tan x) -1)) (fma (tan x) (tan x) -1)) (* (* (- -1 (* (tan x) (tan x))) (- -1 (* (tan x) (tan x)))) (- -1 (* (tan x) (tan x)))))
373.0ms
(log (exp (* (cbrt (/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))) (cbrt (/ (fma (tan x) (tan x) -1) (- -1 (* (tan x) (tan x))))))))
313.0ms
(log (exp (/ (fma (tan x) (tan x) -1) (- (* -1 -1) (* (* (tan x) (tan x)) (* (tan x) (tan x)))))))
258.0ms
(- (+ (* 2/3 (pow x 4)) 1) (* 2 (pow x 2)))

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes228.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.1s1507×body1280valid
1.7s1216×body640valid
1.2s4325×body80valid
550.0ms632×body320valid
130.0ms320×body160valid