Details

Time bar (total: 12.2s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.1b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 476
Calls
4 calls:
119.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
328.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
475.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
280.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
170.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
132.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
72.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify130.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
0.1b
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.3b
(/ 1 (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite955.0ms

Algorithm
rewrite-expression-head
Rules
377×*-un-lft-identity
310×times-frac
147×add-sqr-sqrt
138×add-cube-cbrt
136×distribute-lft-out
85×associate-*l*
54×add-exp-log
34×add-cbrt-cube
24×div-exp
20×associate-/r*
15×div-inv
14×cbrt-undiv
12×prod-exp associate-/l*
9×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r/ unswap-sqr
2×pow-flip flip3-+ pow-prod-down associate-*l/ flip-+ fma-udef
1×distribute-rgt-in distribute-lft-in *-commutative inv-pow
Counts
4 → 305
Calls
4 calls:
183.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
333.0ms
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
169.0ms
(/ 1 (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
252.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series690.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
205.0ms
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
295.0ms
(/ 1 (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify142.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
08885411
144414945
250014943

prune678.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite650.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
84×sqrt-prod
77×times-frac
62×add-sqr-sqrt
56×add-cube-cbrt
39×distribute-lft-out
13×associate-/r*
12×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
1×sqrt-undiv
Counts
4 → 177
Calls
4 calls:
182.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
204.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
127.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
129.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series370.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
93.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
42.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify70.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05272718
119402545
250012473

prune542.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0)))) (/ (cbrt 1) (fma 1.0 2.0 (+ alpha beta))))
0.3b
(/ (* (cbrt 1) (cbrt 1)) (/ (/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0)))) (/ (cbrt 1) (fma 1.0 2.0 (+ alpha beta)))))
15.3b
(/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite405.0ms

Algorithm
rewrite-expression-head
Rules
1925×times-frac
936×*-un-lft-identity
588×add-sqr-sqrt
586×add-cube-cbrt
306×cbrt-prod
274×associate-/r*
210×distribute-lft-out
140×associate-/r/
106×div-inv
97×add-exp-log
74×add-cbrt-cube
70×flip3-+ flip-+
55×cbrt-undiv div-exp
15×prod-exp cbrt-unprod
13×associate-/l*
6×pow1
5×associate-*l*
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l/
2×fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 894
Calls
4 calls:
79.0ms
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
85.0ms
(/ (/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0)))) (/ (cbrt 1) (fma 1.0 2.0 (+ alpha beta))))
97.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0)))) (/ (cbrt 1) (fma 1.0 2.0 (+ alpha beta)))))
63.0ms
(/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
210.0ms
(/ (/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0)))) (/ (cbrt 1) (fma 1.0 2.0 (+ alpha beta))))
149.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0)))) (/ (cbrt 1) (fma 1.0 2.0 (+ alpha beta)))))
119.0ms
(/ (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify268.0ms

Algorithm
egg-herbie
Counts
906 → 906
Iterations

Useful iterations: 1 (59.0ms)

IterNodesCost
0352123066
1500122662

prune3.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes73.0ms

Accuracy

68.2% (1.2b remaining)

Error of 1.3b against oracle of 0.1b and baseline of 3.9b

bsearch80.0ms

Steps
ItersRangePoint
10
6.334284910020751e+152
7.013797287950175e+165
1.3288970919019584e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03928
13928

end0.0ms

sample551.0ms

Algorithm
intervals
Results
287.0ms8000×body80valid
85.0ms8000×pre80true