Details

Time bar (total: 19.5s)

sample191.0ms

Algorithm
intervals
Results
53.0ms46×body1280valid
26.0ms34×body640valid
21.0ms139×body80valid
10.0ms21×body320valid
5.0ms16×body160valid

simplify143.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
0715
11315
22214
32914
43714
54214
64414
done4414

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.1b
(fma (tan x) (tan x) 1.0)
0.1b
(- 1.0 (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
12×times-frac
11×pow1
8×add-exp-log add-cbrt-cube
6×add-log-exp
5×difference-of-squares
4×tan-quot expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-neg swap-sqr associate-*r* associate-*l* prod-diff associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv pow2 frac-times sub-neg frac-2neg pow-plus diff-log div-sub associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef div-inv unswap-sqr
Counts
4 → 97
Calls
4 calls:
32.0ms
(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
1.0ms
(fma (tan x) (tan x) 1.0)
14.0ms
(- 1.0 (* (tan x) (tan x)))
54.0ms
(* (tan x) (tan x))

series376.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
69.0ms
(fma (tan x) (tan x) 1.0)
60.0ms
(- 1.0 (* (tan x) (tan x)))
89.0ms
(* (tan x) (tan x))

simplify2.5s

Counts
109 → 109
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01551557
13301462
28901345
328061320
done50001314

prune433.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0))
0.1b
(fma (tan x) (tan x) 1.0)
0.3b
(fma (tan x) (- (tan x)) 1.0)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 49
Calls
3 calls:
11.0ms
(/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0))
1.0ms
(fma (tan x) (tan x) 1.0)
1.0ms
(fma (tan x) (- (tan x)) 1.0)

series334.0ms

Counts
3 → 9
Calls
3 calls:
196.0ms
(/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0))
57.0ms
(fma (tan x) (tan x) 1.0)
81.0ms
(fma (tan x) (- (tan x)) 1.0)

simplify2.3s

Counts
58 → 58
Iterations

Useful iterations: 3 (260.0ms)

IterNodesCost
087978
1160967
2378883
3985882
43069882
done5001882

prune286.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (tan x) (tan x) 1.0)
0.1b
(expm1 (log1p (/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0))))
0.3b
(log1p (/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0)))
0.3b
(fma (tan x) (- (tan x)) 1.0)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×expm1-log1p-u
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
2×fma-udef
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 42
Calls
4 calls:
0.0ms
(fma (tan x) (tan x) 1.0)
0.0ms
(expm1 (log1p (/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0))))
1.0ms
(log1p (/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0)))
0.0ms
(fma (tan x) (- (tan x)) 1.0)

series936.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(fma (tan x) (tan x) 1.0)
485.0ms
(expm1 (log1p (/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0))))
326.0ms
(log1p (/ (fma (tan x) (- (tan x)) 1.0) (fma (tan x) (tan x) 1.0)))
60.0ms
(fma (tan x) (- (tan x)) 1.0)

simplify2.6s

Counts
54 → 54
Iterations

Useful iterations: done (2.6s)

IterNodesCost
092886
1174855
2416761
31199755
44235751
done5000749

prune321.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1.0 (* (tan x) (tan x)))
0.2b
(/ 1 (fma (tan x) (tan x) 1.0))
0.2b
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
0.3b
(* (tan x) (tan x))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
27×*-un-lft-identity
26×add-cube-cbrt
20×times-frac
19×add-exp-log
16×associate-*r*
14×pow1
13×add-cbrt-cube
7×associate-*l*
6×add-log-exp
5×prod-exp
4×tan-quot expm1-log1p-u div-exp log1p-expm1-u unswap-sqr
3×frac-times flip3-- fma-neg swap-sqr prod-diff associate-*l/ associate-/r* flip-- cbrt-unprod associate-/l*
2×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down *-commutative div-inv difference-of-squares
1×pow2 sub-neg pow-flip frac-2neg pow-plus diff-log clear-num pow-sqr un-div-inv pow-prod-up inv-pow
Counts
4 → 127
Calls
4 calls:
13.0ms
(- 1.0 (* (tan x) (tan x)))
12.0ms
(/ 1 (fma (tan x) (tan x) 1.0))
31.0ms
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
34.0ms
(* (tan x) (tan x))

series386.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- 1.0 (* (tan x) (tan x)))
131.0ms
(/ 1 (fma (tan x) (tan x) 1.0))
134.0ms
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
60.0ms
(* (tan x) (tan x))

simplify3.1s

Counts
139 → 139
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01892015
13981781
210791587
336491550
done50001546

prune531.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
done916

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.5s1546×body1280valid
1.1s1198×body640valid
902.0ms647×body320valid
625.0ms4315×body80valid
128.0ms294×body160valid