Details

Time bar (total: 35.9s)

sample422.0ms

Algorithm
intervals
Results
98.0ms47×body1280valid
95.0ms46×body640valid
71.0ms21×body320valid
55.0ms162×body80valid
16.0ms52×body80nan
9.0ms11×body160valid

simplify1.4s

Counts
1 → 1

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.7b

localize50.0ms

Local error

Found 4 expressions with local error:

14.4b
(pow (fma 2 x (fma F F 2)) -1/2)
6.9b
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
0.1b
(/ x (tan B))
0.1b
(/ F (sin B))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
31×*-un-lft-identity add-cube-cbrt
30×times-frac
22×add-exp-log
13×add-cbrt-cube associate-*r*
8×unpow-prod-down
7×associate-*l*
6×associate-/r* prod-exp associate-/l* unswap-sqr
5×pow1 div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp cbrt-undiv pow-unpow pow-exp div-inv
2×clear-num frac-2neg cbrt-unprod
1×pow-pow tan-quot associate-*r/ associate-/r/ *-commutative
Counts
4 → 127
Calls
4 calls:
Slowest
26.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
5.0ms
(/ x (tan B))
5.0ms
(/ F (sin B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series789.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
312.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
238.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
147.0ms
(/ x (tan B))
91.0ms
(/ F (sin B))

simplify2.4s

Counts
139 → 139

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.8b

localize50.0ms

Local error

Found 4 expressions with local error:

14.4b
(pow (fma 2 x (fma F F 2)) -1/2)
0.3b
(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b
(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
0.1b
(/ x (tan B))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
56×add-exp-log
31×prod-exp
29×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube
18×times-frac
16×associate-*r*
9×div-exp
8×associate-*l*
7×pow1 unpow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow associate-/r* associate-/l* unswap-sqr sqr-pow
2×*-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down tan-quot associate-*r/ associate-/r/ un-div-inv
Counts
4 → 127
Calls
4 calls:
Slowest
39.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
17.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) F)
5.0ms
(/ x (tan B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series742.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
266.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
202.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
142.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) F)
132.0ms
(/ x (tan B))

simplify923.0ms

Counts
139 → 139

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.8b

localize87.0ms

Local error

Found 4 expressions with local error:

14.4b
(pow (fma 2 x (fma F F 2)) -1/2)
3.4b
(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
0.3b
(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b
(* (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (/ 1 (sin B)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
19×add-exp-log
18×*-un-lft-identity
17×add-cube-cbrt
16×associate-*r*
11×times-frac add-cbrt-cube
10×associate-*l*
7×pow1 unpow-prod-down prod-exp
6×unswap-sqr
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow cbrt-unprod sqr-pow
2×pow-to-exp div-exp pow-exp *-commutative
1×cbrt-undiv rec-exp log1p-udef pow-pow 1-exp pow-prod-down log1p-expm1 associate-*r/ un-div-inv div-inv
Counts
4 → 99
Calls
4 calls:
Slowest
32.0ms
(* (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (/ 1 (sin B)))
17.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) F)
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms
(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
649.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
605.0ms
(* (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (/ 1 (sin B)))
248.0ms
(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
140.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify2.3s

Counts
111 → 111

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.3b

localize54.0ms

Local error

Found 4 expressions with local error:

14.4b
(pow (fma 2 x (fma F F 2)) -1/2)
0.3b
(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b
(/ (* x (cos B)) (sin B))
0.2b
(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
32×prod-exp
23×add-sqr-sqrt add-cbrt-cube
18×*-un-lft-identity add-cube-cbrt
16×associate-*r*
12×times-frac
10×div-exp
8×associate-*l* cbrt-unprod
7×pow1 unpow-prod-down
6×pow-to-exp pow-exp
4×expm1-log1p-u cbrt-undiv rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* unswap-sqr sqr-pow
2×*-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down associate-*r/ un-div-inv associate-/l*
Counts
4 → 120
Calls
4 calls:
Slowest
25.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
15.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) F)
13.0ms
(/ (* x (cos B)) (sin B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series796.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
304.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
228.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
146.0ms
(/ (* x (cos B)) (sin B))
118.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify918.0ms

Counts
132 → 132

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

regimes423.0ms

Accuracy

56.7% (2.5b remaining)

Error of 7.7b against oracle of 5.2b and baseline of 10.9b

bsearch264.0ms

end0.0ms

sample14.1s

Algorithm
intervals
Results
5.2s1652×body1280valid
3.2s1337×body640valid
3.0s4818×body80valid
1.3s718×body320valid
674.0ms1640×body80nan
332.0ms348×body160valid