Details

Time bar (total: 1.0m)

sample106.0ms

Algorithm
intervals
Results
36.0ms55×body2560valid
20.0ms23×body320valid
18.0ms46×body1280valid
16.0ms48×body640valid
5.0ms69×body80valid
3.0ms15×body160valid

simplify39.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
39.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize23.0ms

Local error

Found 2 expressions with local error:

16.2b
(/ (- 1 (cos x)) (* x x))
1.7b
(- 1 (cos x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-log-exp
3×fma-neg distribute-lft-out--
2×expm1-log1p-u pow1 cbrt-undiv flip3-- div-exp insert-posit16 log1p-expm1-u flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
2 → 63
Calls
2 calls:
Slowest
36.0ms
(/ (- 1 (cos x)) (* x x))
6.0ms
(- 1 (cos x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
62.0ms
(/ (- 1 (cos x)) (* x x))
38.0ms
(- 1 (cos x))

simplify6.8s

Counts
90 → 69
Calls
90 calls:
Slowest
737.0ms
(* (* (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x))) (/ (- 1 (cos x)) (* x x)))
723.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
681.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
400.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
396.0ms
(* (* x x) (+ (* 1 1) (+ (* (cos x) (cos x)) (* 1 (cos x)))))

prune557.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

16.1b
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.4b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.2b
(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
25×*-un-lft-identity
22×times-frac
17×add-sqr-sqrt
15×add-cube-cbrt
12×cbrt-undiv div-exp
11×pow1 associate-/l*
7×prod-exp cbrt-unprod
6×associate-/r/ add-log-exp
5×associate-/r* distribute-lft-out
4×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u div-inv
3×fma-def div-sub swap-sqr associate-*r* associate-*l* sqr-sin
2×clear-num frac-2neg sin-mult associate-/l/
1×pow2 +-commutative sum-log pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 126
Calls
4 calls:
Slowest
31.0ms
(/ (* (sin x) (sin x)) (+ 1 (cos x)))
23.0ms
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
20.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series239.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
71.0ms
(/ (* (sin x) (sin x)) (+ 1 (cos x)))
32.0ms
(* (sin x) (sin x))
19.0ms
(+ 1 (cos x))

simplify18.8s

Counts
156 → 138
Calls
156 calls:
Slowest
753.0ms
(/ (/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* x x) x) (* (* x x) x)))
715.0ms
(/ (* x x) (/ (* (sin x) (sin x)) (+ 1 (cos x))))
713.0ms
(/ (/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* x x) x) (* (* x x) x)))
704.0ms
(/ (/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* x x) (* x x)) (* x x)))
650.0ms
(/ (/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* x x) (* x x)) (* x x)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ 1 (cos x))
0.1b
(* (/ (sin x) x) (/ (sin x) x))
0.1b
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x)))
0.1b
(/ (sin x) x)

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
53×times-frac
49×*-un-lft-identity
43×add-cube-cbrt
36×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×swap-sqr associate-*r* associate-*l*
11×pow1
8×prod-exp cbrt-unprod
7×associate-/r*
6×div-inv add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* unswap-sqr
3×fma-def distribute-lft-out associate-/l/
2×frac-times clear-num frac-2neg flip3-+ associate-*l/ associate-*r/ associate-/r/ flip-+
1×pow2 +-commutative sum-log pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
Counts
4 → 155
Calls
4 calls:
Slowest
31.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x)))
27.0ms
(* (/ (sin x) x) (/ (sin x) x))
7.0ms
(/ (sin x) x)
5.0ms
(+ 1 (cos x))

series199.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x)))
54.0ms
(* (/ (sin x) x) (/ (sin x) x))
45.0ms
(/ (sin x) x)
13.0ms
(+ 1 (cos x))

simplify18.5s

Counts
196 → 167
Calls
196 calls:
Slowest
1.2s
(* (* (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x))) (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x)))) (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x))))
619.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
606.0ms
(* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))
583.0ms
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x))))
534.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

16.1b
(/ (* (sin x) (tan (/ x 2))) (* x x))
0.2b
(* (sin x) (tan (/ x 2)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
6×add-sqr-sqrt
5×prod-exp cbrt-unprod
4×pow1 cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
3×associate-*r* associate-*l*
2×expm1-log1p-u tan-quot associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
1×clear-num associate-/r* frac-2neg times-frac pow-prod-down *-commutative div-inv associate-/l* unswap-sqr associate-/l/
Counts
2 → 47
Calls
2 calls:
Slowest
17.0ms
(/ (* (sin x) (tan (/ x 2))) (* x x))
16.0ms
(* (sin x) (tan (/ x 2)))

series230.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
125.0ms
(/ (* (sin x) (tan (/ x 2))) (* x x))
105.0ms
(* (sin x) (tan (/ x 2)))

simplify6.1s

Counts
55 → 53
Calls
55 calls:
Slowest
939.0ms
(/ (* (* (* (sin x) (tan (/ x 2))) (* (sin x) (tan (/ x 2)))) (* (sin x) (tan (/ x 2)))) (* (* (* x x) x) (* (* x x) x)))
536.0ms
(/ (* (* (* (sin x) (tan (/ x 2))) (* (sin x) (tan (/ x 2)))) (* (sin x) (tan (/ x 2)))) (* (* (* x x) (* x x)) (* x x)))
446.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2)))) (* (* (* x x) x) (* (* x x) x)))
433.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))))
406.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))

prune466.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.1s1615×body2560valid
870.0ms1460×body640valid
798.0ms1314×body1280valid
345.0ms907×body320valid
289.0ms2202×body80valid
143.0ms502×body160valid