Details

Time bar (total: 11.4s)

sample28.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms256×pre80true

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

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) (* beta alpha))
0.0b
(/ (/ (+ (+ (+ 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)))

rewrite114.0ms

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
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 475
Calls
4 calls:
6.0ms
(+ (+ alpha beta) (* beta alpha))
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms
(/ (/ (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
142.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms
(/ (/ (/ (+ (+ (+ 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))
81.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify135.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0153413079
1500112129

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
16.4b
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
934×times-frac
557×*-un-lft-identity
429×add-sqr-sqrt
415×add-cube-cbrt
166×associate-*l*
71×distribute-lft-out
59×associate-/l*
49×add-exp-log add-cbrt-cube
32×div-inv
24×cbrt-undiv div-exp
16×associate-/r/
11×flip3-- flip--
10×associate-/r*
8×prod-diff prod-exp cbrt-unprod associate-/l/
7×distribute-rgt-in distribute-lft-in
6×pow1
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg associate-*r* clear-num
2×sub-neg flip3-+ associate-*l/ associate--l+ flip-+
1×pow-prod-down *-commutative
Counts
4 → 522
Calls
4 calls:
46.0ms
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
25.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
11.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
54.0ms
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
159.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
153.0ms
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

simplify153.0ms

Algorithm
egg-herbie
Counts
534 → 534
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0205412731
1500212127

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite465.0ms

Algorithm
rewrite-expression-head
Rules
1777×times-frac
1545×*-un-lft-identity
761×add-sqr-sqrt
747×sqrt-prod
678×add-cube-cbrt
497×distribute-lft-out
321×associate-*r*
104×associate-/r/
71×associate-/l*
63×associate-*l*
54×flip3-+ flip-+
52×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
11×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 896
Calls
4 calls:
41.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
293.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))
19.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series600.0ms

Counts
4 → 12
Calls
4 calls:
277.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
164.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify279.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0198828172
1500127048

prune2.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
206×*-un-lft-identity
136×add-sqr-sqrt add-cube-cbrt
75×sqrt-prod
41×associate-/l*
35×distribute-lft-out
18×associate-/r*
17×add-exp-log
16×associate-/r/
15×add-cbrt-cube
12×sqrt-div
10×flip3-+ flip-+
8×div-inv
7×div-exp
6×pow1 cbrt-undiv
5×associate-/l/
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×pow-flip
1×rec-exp sqrt-pow1 pow1/2 1-exp inv-pow
Counts
4 → 280
Calls
4 calls:
8.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
23.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series444.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
205.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
70.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
100.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify117.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
09245167
141094735
250024724

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.2b

regimes83.0ms

Accuracy

57.6% (1.1b remaining)

Error of 2.2b against oracle of 1.2b and baseline of 3.7b

bsearch72.0ms

Steps
ItersRangePoint
9
3.0600113586025243e+158
5.175601966716431e+167
3.2321215175226654e+162

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04238
14238

end0.0ms

sample569.0ms

Algorithm
intervals
Results
314.0ms8000×body80valid
107.0ms8000×pre80true