Details

Time bar (total: 14.5s)

sample24.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
7.0ms276×body80nan

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0217
1416
2696
3956
41256
51406
61426
71426

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (sqrt x) 4.0 (+ x 1.0))
0.0b
(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
0.0b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
95×add-sqr-sqrt *-un-lft-identity
67×add-cube-cbrt
16×associate-/r*
14×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num associate-/l/
1×flip3-- div-sub associate-/r/ flip-- fma-udef
Counts
3 → 142
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
12.0ms
(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
2.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

series163.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
78.0ms
(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
49.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

simplify85.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
06271691
123791609
250021609

prune354.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (sqrt x) 4.0 (+ x 1.0))
0.0b
(* (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
0.0b
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
37×*-un-lft-identity
31×times-frac
23×add-cube-cbrt
19×associate-*l*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l*
3×expm1-log1p-u associate-*r* associate-/r* log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×flip3-- frac-2neg div-sub pow-prod-down associate-*l/ clear-num *-commutative flip-- fma-udef
Counts
3 → 90
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
15.0ms
(* (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
8.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series192.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
79.0ms
(* (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
73.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify51.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0357827
11182752
25001738

prune233.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))) 6.0)
0.0b
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
0.0b
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.1b
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
227×add-sqr-sqrt
200×sqrt-prod
197×*-un-lft-identity
180×times-frac
93×add-cube-cbrt
61×associate-*r*
52×difference-of-squares
38×add-exp-log add-cbrt-cube
35×associate-*l*
26×distribute-lft-out distribute-lft-out--
14×associate-/l*
13×prod-exp cbrt-unprod
12×associate-/r*
11×pow1
10×cbrt-undiv div-exp
9×unswap-sqr
5×associate-*l/
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv associate-/l/ add-log-exp
2×frac-times frac-2neg associate-*r/ clear-num *-commutative
1×flip3-- flip3-+ div-sub flip-- flip-+
Counts
4 → 295
Calls
4 calls:
74.0ms
(* (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))) 6.0)
85.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
17.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
22.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
439.0ms
(* (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))) 6.0)
367.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
238.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
249.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify87.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010325867
150015258

prune741.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))) (cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))))
0.1b
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
0.1b
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
0.1b
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-div
20×frac-times
14×associate-*r/ associate-*l/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u swap-sqr associate-*r* associate-*l* add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 90
Calls
4 calls:
9.0ms
(* (cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))) (cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))))
17.0ms
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
17.0ms
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
18.0ms
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))

series9.5s

Counts
4 → 12
Calls
4 calls:
3.4s
(* (cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))) (cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))))
1.9s
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
2.2s
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
2.0s
(cbrt (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015985580
150025225

prune584.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0126
1126

end0.0ms

sample597.0ms

Algorithm
intervals
Results
231.0ms8000×body80valid
194.0ms7781×body80nan