Details

Time bar (total: 16.1s)

sample36.0ms

Algorithm
intervals
Results
18.0ms80×body1280valid
6.0ms144×body80valid
2.0ms12×body640valid
1.0ms10×body320valid
1.0ms10×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1266
2336
3356
4416
5446
6446

prune2.0ms

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: 15.2b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
3.1b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
21×add-cube-cbrt
12×prod-diff
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-def fma-neg associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series856.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
280.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
104.0ms
(/ 1.0 (hypot 1.0 x))
365.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05331129
12036878
25001876

prune245.0ms

Filtered
104 candidates to 84 candidates (80.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1013104
Fresh000
Picked101
Done000
Total1023105

Merged error: 14.4b

Counts
105 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
2.5b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×+-commutative flip3-+ sum-log flip-+ fma-udef distribute-lft-out
Counts
4 → 85
Calls
4 calls:
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
1.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series485.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
110.0ms
(/ 1.0 (hypot 1.0 x))
104.0ms
(/ 1.0 (hypot 1.0 x))
153.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0319561
11141522
25001520

prune292.0ms

Filtered
97 candidates to 85 candidates (87.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh112
Picked011
Done000
Total973100

Merged error: 0.4b

Counts
100 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.6b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
2.5b
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
246×add-sqr-sqrt
176×*-un-lft-identity
168×prod-diff
157×unpow-prod-down cube-prod
126×add-cube-cbrt
84×times-frac
80×difference-of-squares
68×sqr-pow
28×cube-mult unpow3 associate-/l*
26×sqrt-prod
25×distribute-lft-out--
12×fma-neg
9×add-exp-log add-cbrt-cube
8×pow1
6×associate-/r* add-log-exp
5×difference-cubes
4×expm1-log1p-u pow-pow log1p-expm1-u
3×pow-unpow
2×cbrt-undiv cube-div flip3-- frac-2neg sqrt-pow1 sqrt-div associate-*r/ div-exp clear-num flip-- div-inv associate-/l/
1×pow-to-exp sub-neg flip3-+ pow1/2 diff-log div-sub pow-prod-down pow-exp sqrt-pow2 flip-+ rem-cube-cbrt
Counts
4 → 398
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
26.0ms
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
12.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
16.0ms
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

series7.8s

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ 1.0 (hypot 1.0 x))
5.6s
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
876.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.2s
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

simplify174.0ms

Algorithm
egg-herbie
Counts
410 → 410
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0243912052
1500110922

prune874.0ms

Filtered
410 candidates to 157 candidates (38.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New4091410
Fresh011
Picked101
Done011
Total4103413

Merged error: 0.4b

Counts
413 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.6b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.6b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
2.4b
(+ (pow 1.0 6) (- (* (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×pow1
15×add-sqr-sqrt add-cube-cbrt unpow-prod-down
12×pow-pow cube-prod
9×pow-unpow
8×add-log-exp
7×add-exp-log fma-def add-cbrt-cube
6×cube-div sqrt-pow1 sqrt-div associate-*r/ sqrt-prod
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u sqr-pow
3×cube-mult pow-to-exp pow1/2 unpow3 pow-prod-down pow-exp sqrt-pow2 rem-cube-cbrt
2×sum-log
1×+-commutative neg-sub0 associate-+r- unsub-neg neg-log distribute-lft-out
Counts
4 → 124
Calls
4 calls:
8.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
8.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
8.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
6.0ms
(+ (pow 1.0 6) (- (* (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))

series3.1s

Counts
4 → 12
Calls
4 calls:
691.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
885.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
694.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
821.0ms
(+ (pow 1.0 6) (- (* (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))

simplify93.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06181542
128141387
250011367

prune542.0ms

Filtered
136 candidates to 87 candidates (64.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1342136
Fresh011
Picked101
Done011
Total1354139

Merged error: 0.4b

Counts
139 → 4

regimes229.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.8b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04235
14235

end0.0ms

sample1.1s

Algorithm
intervals
Results
625.0ms2855×body1280valid
163.0ms4050×body80valid
115.0ms625×body640valid
39.0ms322×body320valid
12.0ms148×body160valid

Profiling

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