Details

Time bar (total: 1.3m)

sample51.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
18.0ms268×body80nan

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0217
1416
2696
3956
41256
51406
61426
71426

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
94×add-sqr-sqrt *-un-lft-identity
66×add-cube-cbrt
16×associate-/r*
14×distribute-lft-out-- difference-of-squares
9×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
4×cbrt-undiv div-exp
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
1×flip3-- div-sub associate-/r/ flip--
Counts
2 → 132
Calls
2 calls:
2.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
12.0ms
(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

series148.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
94.0ms
(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

simplify88.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
06151625
123521553
250021553

prune359.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) (/ 1 6.0))
0.0b
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
652×times-frac
370×add-sqr-sqrt *-un-lft-identity
278×add-cube-cbrt
46×distribute-lft-out-- difference-of-squares
36×div-inv
26×add-exp-log
24×associate-/l*
17×div-exp
16×associate-/r* add-cbrt-cube
9×cbrt-undiv
3×div-sub associate-/l/
2×pow1 expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
1×flip3-- associate-/r/ flip--
Counts
2 → 346
Calls
2 calls:
18.0ms
(/ (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) (/ 1 6.0))
12.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series174.0ms

Counts
2 → 6
Calls
2 calls:
88.0ms
(/ (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) (/ 1 6.0))
86.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify96.0ms

Algorithm
egg-herbie
Counts
352 → 352
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
016005720
150015270

prune729.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 6.0) (/ (- (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))))
0.0b
(/ (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (/ 1 6.0) (/ (- (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))))

rewrite7.3s

Algorithm
rewrite-expression-head
Rules
119961×times-frac
68905×*-un-lft-identity
61921×add-sqr-sqrt
50171×sqrt-prod
39353×add-cube-cbrt
11284×difference-of-squares
9134×distribute-lft-out
5642×distribute-lft-out--
3357×div-inv
829×associate-/r*
103×add-exp-log
77×div-exp
61×add-cbrt-cube associate-/l*
41×cbrt-undiv
37×associate-/r/
6×rec-exp 1-exp associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×flip3-- flip3-+ div-sub flip-- flip-+
Counts
4 → 27635
Calls
4 calls:
44.0ms
(/ (/ 1 6.0) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
18.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
720.0ms
(/ (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (/ 1 6.0) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
26.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
671.0ms
(/ (/ 1 6.0) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
253.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
454.0ms
(/ (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (/ 1 6.0) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
267.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify11.4s

Algorithm
egg-herbie
Counts
27647 → 27647
Iterations

Useful iterations: 0 (222.0ms)

IterNodesCost
0129931240103

prune49.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x 1.0) (sqrt (/ 1 6.0)))
0.0b
(/ 1 (fma (sqrt x) 4.0 (+ x 1.0)))
0.2b
(/ (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (/ 1 6.0)))
0.7b
(* (/ (- x 1.0) (sqrt (/ 1 6.0))) (/ (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (/ 1 6.0))))

rewrite383.0ms

Algorithm
rewrite-expression-head
Rules
1432×times-frac
938×add-sqr-sqrt
696×*-un-lft-identity
582×add-cube-cbrt
578×sqrt-prod
213×associate-*r*
85×associate-*l*
76×div-inv
65×unswap-sqr
54×add-exp-log
35×associate-/r*
34×add-cbrt-cube
33×distribute-lft-out-- difference-of-squares
26×div-exp
21×associate-/l*
14×cbrt-undiv
10×prod-exp
7×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp sqrt-div 1-exp associate-/r/ log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
1×frac-times flip3-- pow-flip div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- inv-pow
Counts
4 → 802
Calls
4 calls:
14.0ms
(/ (- x 1.0) (sqrt (/ 1 6.0)))
2.0ms
(/ 1 (fma (sqrt x) 4.0 (+ x 1.0)))
13.0ms
(/ (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (/ 1 6.0)))
281.0ms
(* (/ (- x 1.0) (sqrt (/ 1 6.0))) (/ (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (/ 1 6.0))))

series621.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (- x 1.0) (sqrt (/ 1 6.0)))
66.0ms
(/ 1 (fma (sqrt x) 4.0 (+ x 1.0)))
169.0ms
(/ (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (/ 1 6.0)))
273.0ms
(* (/ (- x 1.0) (sqrt (/ 1 6.0))) (/ (/ 1 (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (/ 1 6.0))))

simplify188.0ms

Algorithm
egg-herbie
Counts
814 → 814
Iterations

Useful iterations: 1 (65.0ms)

IterNodesCost
0277313059
1500212032

prune2.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

end0.0ms

sample1.4s

Algorithm
intervals
Results
638.0ms8000×body80valid
539.0ms7994×body80nan