Details

Time bar (total: 18.8s)

sample33.0ms

Algorithm
intervals
Results
8.0ms204×body80valid
4.0ms256×pre80true
3.0ms17×body1280valid
3.0ms20×body640valid
1.0ms12×body320valid
0.0ms3×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.6b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity times-frac
62×add-sqr-sqrt
58×add-cube-cbrt
42×fma-def
24×associate-/r/
21×distribute-lft-out
20×add-exp-log add-cbrt-cube
19×flip3-+ flip-+
18×prod-diff
12×div-inv
11×distribute-rgt-in distribute-lft-in
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv div-exp associate-/r*
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×expm1-log1p-u associate-*r/ associate-*l* associate-*l/ log1p-expm1-u
3×prod-exp cbrt-unprod
2×sub-neg frac-2neg clear-num
1×+-commutative pow-prod-down sum-log *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 212
Calls
4 calls:
10.0ms
(* (+ alpha beta) (- beta alpha))
21.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
37.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
16.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (+ alpha beta) (- beta alpha))
236.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
279.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
79.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify56.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09372463
150022158

prune657.0ms

Filtered
224 candidates to 160 candidates (71.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2168224
Fresh000
Picked101
Done000
Total2178225

Merged error: 5.3b

Counts
225 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.6b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
3.2b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
10036×times-frac
6754×*-un-lft-identity
4612×add-sqr-sqrt
3458×add-cube-cbrt
1178×fma-def
1071×distribute-lft-out
577×distribute-lft-out-- difference-of-squares
400×associate-/r/
314×associate-/l*
205×div-inv
164×flip3-+ flip-+
105×associate-/r*
62×add-exp-log
43×div-exp
32×flip3-- add-cbrt-cube flip--
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 3236
Calls
4 calls:
93.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
12.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
27.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
430.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series612.0ms

Counts
4 → 12
Calls
4 calls:
285.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
64.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
146.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
118.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify512.0ms

Algorithm
egg-herbie
Counts
3248 → 3248
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0500147178

prune9.3s

Filtered
3248 candidates to 1754 candidates (54.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New324173248
Fresh347
Picked101
Done000
Total3245113256

Merged error: 5.3b

Counts
3256 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.6b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
12.4b
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
1062×times-frac
759×*-un-lft-identity
595×add-sqr-sqrt
413×add-cube-cbrt
105×associate-/r*
91×distribute-lft-out-- difference-of-squares
82×distribute-lft-out
65×associate-/r/
33×div-inv
32×add-exp-log
27×flip3-+ flip-+
24×associate-/l*
20×add-cbrt-cube
19×div-exp
10×cbrt-undiv
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp frac-2neg 1-exp clear-num
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 591
Calls
4 calls:
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
12.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
26.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series356.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
66.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
152.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
84.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify128.0ms

Algorithm
egg-herbie
Counts
603 → 603
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
016438750
150028070

prune1.7s

Filtered
603 candidates to 325 candidates (53.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New6012603
Fresh01010
Picked101
Done000
Total60212614

Merged error: 5.3b

Counts
614 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.6b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
12.4b
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
1050×times-frac
745×*-un-lft-identity
589×add-sqr-sqrt
407×add-cube-cbrt
101×associate-/r*
91×distribute-lft-out-- difference-of-squares
78×distribute-lft-out
63×associate-/r/
32×div-inv
31×add-exp-log
26×flip3-+ flip-+
21×associate-/l*
19×add-cbrt-cube
18×div-exp
9×cbrt-undiv
6×pow1
5×flip3-- flip--
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down rec-exp pow-unpow 1-exp cube-prod
2×frac-2neg clear-num
1×cube-mult pow-to-exp pow-flip pow-pow unpow3 pow-exp fma-udef associate-/l/ inv-pow rem-cube-cbrt sqr-pow
Counts
4 → 581
Calls
4 calls:
2.0ms
(pow (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
12.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
31.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series459.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(pow (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
67.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
142.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
79.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify134.0ms

Algorithm
egg-herbie
Counts
593 → 593
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
016968945
150018023

prune1.4s

Filtered
593 candidates to 253 candidates (42.7%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New5912593
Fresh11011
Picked011
Done000
Total59213605

Merged error: 5.3b

Counts
605 → 13

regimes326.0ms

Accuracy

15.7% (5.5b remaining)

Error of 11.5b against oracle of 6.0b and baseline of 12.5b

bsearch74.0ms

Steps
ItersRangePoint
8
3.918843472614674e+137
1.0363106199006555e+140
7.328664447613938e+139

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample807.0ms

Algorithm
intervals
Results
243.0ms6350×body80valid
122.0ms8000×pre80true
106.0ms518×body1280valid
87.0ms567×body640valid
47.0ms359×body320valid
18.0ms206×body160valid