Details

Time bar (total: 4.3s)

sample50.0ms

Algorithm
intervals
Results
19.0ms52×body1280valid
10.0ms41×body640valid
8.0ms134×body80valid
2.0ms17×body160valid
2.0ms12×body320valid

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2315
3545
41195
53335
616465
750015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.5b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
68×add-sqr-sqrt
63×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
7×add-log-exp
6×flip3-+ flip-+
5×add-exp-log add-cbrt-cube div-inv
4×associate-/r*
3×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- distribute-lft-out--
Counts
3 → 141
Calls
3 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
44.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series131.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
36.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify53.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03981645
112871235
250011212

prune259.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (exp (* -2.0 x))))
0.4b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
28.5b
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
42×times-frac
40×add-sqr-sqrt
37×add-cube-cbrt
36×sqrt-prod
14×associate-/r*
10×add-exp-log
9×distribute-lft-out
8×add-cbrt-cube
7×pow1
6×sqrt-div associate-/l*
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×pow-flip flip3-+ div-exp flip-+
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×rem-sqrt-square rec-exp 1-exp fma-udef hypot-def inv-pow
Counts
4 → 129
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
7.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series367.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
67.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
45.0ms
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
213.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03821270
113311133
250021081

prune298.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
3.8b
(fma (/ (* (cbrt 2.0) (cbrt 2.0)) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (cbrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
0.0ms
(cbrt 2.0)
1.0ms
(cbrt 2.0)
3.0ms
(cbrt 2.0)
0.0ms
(fma (/ (* (cbrt 2.0) (cbrt 2.0)) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (cbrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series461.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
461.0ms
(fma (/ (* (cbrt 2.0) (cbrt 2.0)) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (cbrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0131424
1361358
21468348
35002334

prune186.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* 1.0 x) (- (fma (pow x 3) 0.33333333333333337 1.0) (* 0.5 2.0)))
0.1b
(fma (pow x 3) 0.33333333333333337 1.0)
1.6b
(- (fma (pow x 3) 0.33333333333333337 1.0) (* 0.5 2.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
9×prod-diff
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×associate--r+
4×fma-neg diff-log
3×pow1 add-exp-log expm1-log1p-u sub-neg add-cbrt-cube fma-udef log1p-expm1-u
2×flip3-- associate--l+ flip--
1×associate--r-
Counts
3 → 57
Calls
3 calls:
10.0ms
(- (* 1.0 x) (- (fma (pow x 3) 0.33333333333333337 1.0) (* 0.5 2.0)))
0.0ms
(fma (pow x 3) 0.33333333333333337 1.0)
3.0ms
(- (fma (pow x 3) 0.33333333333333337 1.0) (* 0.5 2.0))

series257.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(- (* 1.0 x) (- (fma (pow x 3) 0.33333333333333337 1.0) (* 0.5 2.0)))
78.0ms
(fma (pow x 3) 0.33333333333333337 1.0)
61.0ms
(- (fma (pow x 3) 0.33333333333333337 1.0) (* 0.5 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0237482
1886403
25001390

prune161.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes215.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04141
14141

end0.0ms

sample1.6s

Algorithm
intervals
Results
637.0ms1723×body1280valid
341.0ms1252×body640valid
250.0ms4095×body80valid
120.0ms620×body320valid
42.0ms310×body160valid