Details

Time bar (total: 9.5s)

sample84.0ms

Algorithm
intervals
Results
26.0ms83×body1280valid
21.0ms82×body640valid
13.0ms250×body80valid
6.0ms41×body320valid
1.0ms14×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
4×pow1
3×associate-*r* associate-*l*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
2 → 51
Calls
2 calls:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series333.0ms

Counts
2 → 6
Calls
2 calls:
114.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
219.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0202424
1995365
25001359

prune159.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
234×sqrt-prod
216×times-frac
95×add-sqr-sqrt
93×add-cube-cbrt *-un-lft-identity
19×add-exp-log add-cbrt-cube
18×associate-/r*
14×associate-/l*
12×div-inv
7×cbrt-undiv div-exp
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 215
Calls
3 calls:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
12.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series654.0ms

Counts
3 → 9
Calls
3 calls:
110.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
227.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
317.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify80.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06233219
129922787
250012785

prune444.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (sqrt (sqrt 2.0)))
0.3b
(* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1))))
1.0b
(/ 1 (sqrt 2.0))
1.0b
(sqrt (/ 1 (sqrt 2.0)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
101×sqrt-prod
74×add-sqr-sqrt
71×times-frac
57×*-un-lft-identity
53×add-cube-cbrt
25×associate-*l*
15×add-exp-log associate-/r*
13×add-cbrt-cube
11×pow1
7×sqrt-pow1 sqrt-div
6×pow-flip unswap-sqr
5×rem-sqrt-square associate-/l/
4×expm1-log1p-u frac-times flip3-+ associate-*r/ div-exp associate-*r* flip-+ log1p-expm1-u div-inv associate-/l* add-log-exp
3×cbrt-undiv pow1/2
2×frac-2neg associate-*l/ prod-exp clear-num cbrt-unprod inv-pow
1×distribute-rgt-in rec-exp distribute-lft-in 1-exp pow-prod-down *-commutative distribute-lft-out
Counts
4 → 185
Calls
4 calls:
23.0ms
(/ (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (sqrt (sqrt 2.0)))
39.0ms
(* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1))))
4.0ms
(/ 1 (sqrt 2.0))
5.0ms
(sqrt (/ 1 (sqrt 2.0)))

series558.0ms

Counts
4 → 8
Calls
4 calls:
235.0ms
(/ (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (sqrt (sqrt 2.0)))
322.0ms
(* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1))))
0.0ms
(/ 1 (sqrt 2.0))
0.0ms
(sqrt (/ 1 (sqrt 2.0)))

simplify86.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05991968
130661670
250011589

prune566.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
0.2b
(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))
0.3b
(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
0.3b
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
2253×sqrt-prod
1726×times-frac
1186×add-sqr-sqrt
808×add-cube-cbrt *-un-lft-identity
376×associate-*r*
85×unswap-sqr
40×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
33×associate-/r*
30×div-inv
14×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 1077
Calls
4 calls:
6.0ms
(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
20.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))
4.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
276.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
244.0ms
(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
420.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))
362.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
228.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

simplify209.0ms

Algorithm
egg-herbie
Counts
1089 → 1089
Iterations

Useful iterations: 1 (46.0ms)

IterNodesCost
0258221519
1500120240

prune2.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes197.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02314
12314

end0.0ms

sample2.2s

Algorithm
intervals
Results
805.0ms2462×body1280valid
465.0ms2128×body640valid
396.0ms8029×body80valid
154.0ms998×body320valid
55.0ms526×body160valid