Details

Time bar (total: 1.5m)

sample476.0ms

Algorithm
intervals
Results
295.0ms97×body2560valid
110.0ms85×body1280valid
33.0ms44×body640valid
13.0ms20×body320valid
11.0ms256×pre80true
3.0ms9×body160valid
0.0ms1×body80valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize21.0ms

Local error

Found 2 expressions with local error:

2.5b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite65.0ms

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
51.0ms
(- (/ 1 x) (/ 1 (tan x)))
7.0ms
(/ 1 (tan x))

series146.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
95.0ms
(- (/ 1 x) (/ 1 (tan x)))
50.0ms
(/ 1 (tan x))

simplify54.6s

Counts
471 → 268
Calls
471 calls:
Slowest
1.1s
(* (* (- (/ 1 x) (/ 1 (tan x))) (- (/ 1 x) (/ 1 (tan x)))) (- (/ 1 x) (/ 1 (tan x))))
608.0ms
(fma (- (cbrt (/ 1 (tan x)))) (* (cbrt (/ 1 (tan x))) (cbrt (/ 1 (tan x)))) (* (cbrt (/ 1 (tan x))) (* (cbrt (/ 1 (tan x))) (cbrt (/ 1 (tan x))))))
502.0ms
(- (pow (/ 1 x) 3) (pow (/ 1 (tan x)) 3))
502.0ms
(- (* (/ 1 x) (/ 1 x)) (* (/ 1 (tan x)) (/ 1 (tan x))))
415.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) x) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))

prune1.8s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 2 expressions with local error:

0.4b
(* x (fma 1/45 (* x x) 1/3))
0.0b
(fma 1/45 (* x x) 1/3)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×associate-*r* associate-*l* fma-udef
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 34
Calls
2 calls:
Slowest
11.0ms
(* x (fma 1/45 (* x x) 1/3))
0.0ms
(fma 1/45 (* x x) 1/3)

series247.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
155.0ms
(* x (fma 1/45 (* x x) 1/3))
92.0ms
(fma 1/45 (* x x) 1/3)

simplify4.0s

Counts
42 → 40
Calls
42 calls:
Slowest
929.0ms
(* (* (* x (fma 1/45 (* x x) 1/3)) (* x (fma 1/45 (* x x) 1/3))) (* x (fma 1/45 (* x x) 1/3)))
838.0ms
(* (* (* x x) x) (* (* (fma 1/45 (* x x) 1/3) (fma 1/45 (* x x) 1/3)) (fma 1/45 (* x x) 1/3)))
241.0ms
(exp (* x (fma 1/45 (* x x) 1/3)))
185.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
166.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune461.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/3 x)
0.2b
(* 1/45 (* x x))
0.1b
(* (* 1/45 (* x x)) x)
0.0b
(+ (* (* 1/45 (* x x)) x) (* 1/3 x))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×pow-prod-down prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
6×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×*-commutative
2×unswap-sqr
1×+-commutative sum-log fma-def flip3-+ distribute-rgt-out flip-+
Counts
4 → 83
Calls
4 calls:
Slowest
67.0ms
(+ (* (* 1/45 (* x x)) x) (* 1/3 x))
53.0ms
(* (* 1/45 (* x x)) x)
15.0ms
(* 1/45 (* x x))
5.0ms
(* 1/3 x)

series273.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(+ (* (* 1/45 (* x x)) x) (* 1/3 x))
71.0ms
(* (* 1/45 (* x x)) x)
35.0ms
(* 1/45 (* x x))
26.0ms
(* 1/3 x)

simplify8.7s

Counts
94 → 95
Calls
94 calls:
Slowest
1.0s
(* (* (* (* 1/45 1/45) 1/45) (* (* (* x x) x) (* (* x x) x))) (* (* x x) x))
803.0ms
(* (* (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/45 (* x x))) (* (* x x) x))
535.0ms
(* (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/45 (* x x)))
469.0ms
(* (* (* (* 1/45 (* x x)) x) (* (* 1/45 (* x x)) x)) (* (* 1/45 (* x x)) x))
351.0ms
(* (exp (* (* 1/45 (* x x)) x)) (exp (* 1/3 x)))

prune933.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
0.5b
(* (cbrt x) (cbrt x))

rewrite11.0ms

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
8.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
321.0ms
(cbrt x)
311.0ms
(cbrt x)
271.0ms
(* (cbrt x) (cbrt x))
268.0ms
(cbrt x)

simplify1.4s

Counts
111 → 97
Calls
111 calls:
Slowest
146.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
136.0ms
(* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))
132.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
116.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
112.0ms
(* (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt x)))

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

regimes126.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample16.9s

Algorithm
intervals
Results
10.0s3258×body2560valid
4.6s2532×body1280valid
1.1s1242×body640valid
440.0ms625×body320valid
321.0ms8000×pre80true
145.0ms309×body160valid
37.0ms34×body80valid