Details

Time bar (total: 18.5s)

sample407.0ms

Algorithm
intervals
Results
154.0ms41×body640valid
40.0ms22×body320valid
39.0ms43×body1280valid
20.0ms142×body80valid
8.0ms256×pre80true
2.0ms8×body160valid

simplify67.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0911
11411
22010
32310
42410
done2410

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
0.1b
(* e (sin v))
0.1b
(* e (cos v))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×associate-*r* associate-*l*
3×expm1-log1p-u times-frac prod-exp associate-/r* cbrt-unprod log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp pow-prod-down associate-/r/ *-commutative unswap-sqr
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l*
Counts
3 → 65
Calls
3 calls:
61.0ms
(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
23.0ms
(* e (sin v))
27.0ms
(* e (cos v))

series289.0ms

Counts
3 → 9
Calls
3 calls:
130.0ms
(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
75.0ms
(* e (sin v))
83.0ms
(* e (cos v))

simplify1.1s

Counts
74 → 74
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0124767
1313731
21553626
done5001620

prune288.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (cos v) e 1.0))
0.0b
(sqrt (fma (cos v) e 1.0))
0.0b
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
0.1b
(* (/ e (sqrt (fma (cos v) e 1.0))) (/ (sin v) (sqrt (fma (cos v) e 1.0))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
66×times-frac
47×add-cube-cbrt *-un-lft-identity
42×sqrt-prod
22×associate-*r* associate-*l*
18×add-exp-log add-cbrt-cube
9×unswap-sqr
8×pow1
6×associate-/r*
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 146
Calls
4 calls:
2.0ms
(sqrt (fma (cos v) e 1.0))
2.0ms
(sqrt (fma (cos v) e 1.0))
11.0ms
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
68.0ms
(* (/ e (sqrt (fma (cos v) e 1.0))) (/ (sin v) (sqrt (fma (cos v) e 1.0))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (fma (cos v) e 1.0))
83.0ms
(sqrt (fma (cos v) e 1.0))
160.0ms
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
133.0ms
(* (/ e (sqrt (fma (cos v) e 1.0))) (/ (sin v) (sqrt (fma (cos v) e 1.0))))

simplify2.3s

Counts
158 → 158
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02333202
16632988
237332646
done50022626

prune724.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
0.1b
(* (/ e (sqrt (fma (cos v) e 1.0))) (log1p (expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0))))))
0.1b
(expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0))))
0.2b
(log1p (expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0)))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
38×times-frac
33×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
11×add-exp-log add-cbrt-cube
6×pow1 associate-/r*
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*r* associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×log1p-udef expm1-log1p frac-2neg log1p-expm1 pow-prod-down associate-*l/ clear-num *-commutative expm1-udef
Counts
4 → 107
Calls
4 calls:
22.0ms
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
50.0ms
(* (/ e (sqrt (fma (cos v) e 1.0))) (log1p (expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0))))))
1.0ms
(expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0))))
1.0ms
(log1p (expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
786.0ms
(* (/ e (sqrt (fma (cos v) e 1.0))) (log1p (expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0))))))
158.0ms
(expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0))))
189.0ms
(log1p (expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0)))))

simplify1.7s

Counts
119 → 119
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02422722
16012482
230272303
done50002287

prune646.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
0.1b
(* (/ e (sqrt (fma (cos v) e 1.0))) (expm1 (log1p (/ (sin v) (sqrt (fma (cos v) e 1.0))))))
0.1b
(expm1 (log1p (/ (sin v) (sqrt (fma (cos v) e 1.0)))))
0.3b
(log1p (/ (sin v) (sqrt (fma (cos v) e 1.0))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
38×times-frac
33×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
11×add-exp-log add-cbrt-cube
6×pow1 associate-/r*
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
3×associate-*r* associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×log1p-udef expm1-log1p frac-2neg log1p-expm1 pow-prod-down associate-*l/ clear-num *-commutative expm1-udef
Counts
4 → 107
Calls
4 calls:
11.0ms
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
27.0ms
(* (/ e (sqrt (fma (cos v) e 1.0))) (expm1 (log1p (/ (sin v) (sqrt (fma (cos v) e 1.0))))))
0.0ms
(expm1 (log1p (/ (sin v) (sqrt (fma (cos v) e 1.0)))))
1.0ms
(log1p (/ (sin v) (sqrt (fma (cos v) e 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (sin v) (sqrt (fma (cos v) e 1.0)))
931.0ms
(* (/ e (sqrt (fma (cos v) e 1.0))) (expm1 (log1p (/ (sin v) (sqrt (fma (cos v) e 1.0))))))
240.0ms
(expm1 (log1p (/ (sin v) (sqrt (fma (cos v) e 1.0)))))
202.0ms
(log1p (/ (sin v) (sqrt (fma (cos v) e 1.0))))

simplify1.7s

Counts
119 → 119
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02422722
16062481
230502305
done50012289

prune572.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes92.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
11320
done1320

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.0s1471×body1280valid
1.3s1272×body640valid
639.0ms4343×body80valid
340.0ms615×body320valid
318.0ms8000×pre80true
73.0ms299×body160valid