Details

Time bar (total: 1.8m)

sample467.0ms

Algorithm
intervals
Results
253.0ms105×body2560valid
151.0ms83×body1280valid
29.0ms39×body640valid
11.0ms256×pre80true
10.0ms20×body320valid
2.0ms5×body160valid
1.0ms4×body80valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize21.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
232×add-sqr-sqrt
224×*-un-lft-identity
208×add-cube-cbrt
182×prod-diff
33×div-inv
14×tan-quot associate-/r/
13×fma-neg
9×difference-of-squares
7×distribute-lft-out--
6×add-exp-log
4×add-cbrt-cube add-log-exp
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
1×cbrt-undiv rec-exp clear-num sub-neg frac-2neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
2 → 262
Calls
2 calls:
Slowest
36.0ms
(- (/ 1 x) (/ 1 (tan x)))
17.0ms
(/ 1 (tan x))

series136.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
103.0ms
(- (/ 1 x) (/ 1 (tan x)))
33.0ms
(/ 1 (tan x))

simplify51.7s

Counts
440 → 268
Calls
440 calls:
Slowest
608.0ms
(fma (/ (sqrt 1) (sqrt x)) (/ (sqrt 1) (sqrt x)) (- (* (/ (sqrt 1) (cbrt (tan x))) (/ (sqrt 1) (* (cbrt (tan x)) (cbrt (tan x)))))))
456.0ms
(fma (- (/ (cbrt 1) (cbrt (tan x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))))
433.0ms
(fma (/ (sqrt 1) (* (cbrt x) (cbrt x))) (/ (sqrt 1) (cbrt x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
430.0ms
(fma (- (/ (cbrt 1) (cbrt (tan x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))))
430.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))

prune1.9s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (fma x (* 1/45 x) 1/3))
0.2b
(* 1/45 x)
0.0b
(fma x (* 1/45 x) 1/3)
0.0b
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in
Counts
4 → 66
Calls
4 calls:
Slowest
11.0ms
(* x (fma x (* 1/45 x) 1/3))
10.0ms
(* 1/45 x)
0.0ms
(fma x (* 1/45 x) 1/3)
0.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(* x (fma x (* 1/45 x) 1/3))
98.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))
97.0ms
(fma x (* 1/45 x) 1/3)
26.0ms
(* 1/45 x)

simplify2.9s

Counts
33 → 78
Calls
33 calls:
Slowest
787.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
389.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
366.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
318.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
201.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune801.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))))
0.2b
(* 1/45 x)
0.2b
(* 1/45 x)
0.0b
(* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×pow1
18×sqrt-prod
17×*-un-lft-identity add-cube-cbrt
15×add-cbrt-cube associate-*l* add-exp-log
13×associate-*r*
8×sqrt-pow1 pow1/2 swap-sqr pow-prod-down
7×unswap-sqr
6×prod-exp cbrt-unprod
5×pow-prod-up
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×pow-sqr
1×pow2 rem-square-sqrt pow-plus sqrt-unprod
Counts
4 → 116
Calls
4 calls:
Slowest
31.0ms
(* x (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))))
12.0ms
(* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3)))
5.0ms
(* 1/45 x)
5.0ms
(* 1/45 x)

series269.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(* x (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))))
74.0ms
(* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3)))
27.0ms
(* 1/45 x)
22.0ms
(* 1/45 x)

simplify3.9s

Counts
101 → 128
Calls
101 calls:
Slowest
327.0ms
(* (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))))
241.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
206.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
205.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
170.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
0.6b
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
0.6b
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
0.5b
(* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))
2.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
1.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
1.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))

series943.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
242.0ms
(* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))
239.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
235.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
227.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))

simplify23.2s

Counts
65 → 97
Calls
65 calls:
Slowest
779.0ms
(* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))
551.0ms
(cbrt (* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))
550.0ms
(* (sqrt (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))) (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))
528.0ms
(* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))
507.0ms
(* (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))) (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes97.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample16.6s

Algorithm
intervals
Results
9.7s3237×body2560valid
4.4s2531×body1280valid
1.6s1234×body640valid
354.0ms639×body320valid
323.0ms8000×pre80true
120.0ms319×body160valid
7.0ms40×body80valid