Details

Time bar (total: 15.4s)

sample26.0ms

Algorithm
intervals
Results
12.0ms256×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: 2.6b

localize11.0ms

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))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite623.0ms

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:
16.0ms
(+ (+ alpha beta) (* beta alpha))
172.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
259.0ms
(/ (/ (/ (+ (+ (+ 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))
146.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series567.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
138.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
337.0ms
(/ (/ (/ (+ (+ (+ 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))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify130.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize19.0ms

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)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
14.6b
(* (/ (/ (/ (+ (+ (+ 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)))

rewrite811.0ms

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:
178.0ms
(/ (* (/ (/ (/ (+ (+ (+ 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))
173.0ms
(/ (/ (/ (+ (+ (+ 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)))
129.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
294.0ms
(* (/ (/ (/ (+ (+ (+ 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)))

series542.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (* (/ (/ (/ (+ (+ (+ 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))
155.0ms
(/ (/ (/ (+ (+ (+ 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)))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
147.0ms
(* (/ (/ (/ (+ (+ (+ 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)))

simplify150.0ms

Algorithm
egg-herbie
Counts
534 → 534
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0205412731
1500212127

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ 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
(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
2.5b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.6b
(* (/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite995.0ms

Algorithm
rewrite-expression-head
Rules
4260×times-frac
2105×*-un-lft-identity
1738×add-sqr-sqrt
1709×add-cube-cbrt
553×associate-*l*
197×distribute-lft-out
187×associate-/l*
165×associate-/r/
121×add-exp-log
95×div-inv
77×div-exp
67×add-cbrt-cube
65×flip3-+ flip-+
37×cbrt-undiv
18×prod-exp
11×flip3-- associate-/r* flip--
10×cbrt-unprod
8×prod-diff
7×distribute-rgt-in distribute-lft-in unswap-sqr
6×pow1 rec-exp 1-exp associate-/l/
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* clear-num
2×sub-neg associate-*l/ associate--l+
1×pow-prod-down *-commutative
Counts
4 → 1446
Calls
4 calls:
181.0ms
(/ (* (/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ 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))
176.0ms
(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
61.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
415.0ms
(* (/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

series573.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (* (/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ 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))
162.0ms
(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
95.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
155.0ms
(* (/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

simplify371.0ms

Algorithm
egg-herbie
Counts
1458 → 1458
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500139183

prune5.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
1.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite321.0ms

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity
52×times-frac
34×add-sqr-sqrt
32×add-cube-cbrt
20×add-exp-log add-cbrt-cube associate-/l*
14×distribute-lft-out
9×add-log-exp
7×cbrt-undiv div-exp
6×pow1
5×associate-*l*
4×expm1-log1p-u fma-def flip3-+ associate-*l/ associate-/r* flip-+ log1p-expm1-u div-inv
3×associate-*r* prod-exp sum-log cbrt-unprod associate-/l/
2×frac-2neg clear-num associate-/r/ fma-udef
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 136
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
30.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
142.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
129.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
36.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
333.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
83.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify81.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06121863
130061619
250011609

prune387.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

68.9% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.8b

bsearch63.0ms

Steps
ItersRangePoint
8
1.1016365673166607e+161
1.0797445965029766e+164
1.1125280590322559e+161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04646
14646

end0.0ms

sample501.0ms

Algorithm
intervals
Results
280.0ms8000×body80valid
89.0ms8000×pre80true