Details

Time bar (total: 7.3s)

sample323.0ms

Algorithm
intervals
Results
35.0ms173×body10240exit
13.0ms381×body80nan
8.0ms237×body80valid
2.0ms23×body160valid

simplify71.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1287
2417
3757
41827
55767
626667
750017

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.1b
(- (exp (* 2.0 x)) 1.0)
5.2b
(- (exp x) 1.0)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
89×*-un-lft-identity
51×times-frac
41×add-cube-cbrt
31×sqrt-prod
24×distribute-lft-out-- difference-of-squares
18×prod-diff
8×add-log-exp
6×add-exp-log fma-neg add-cbrt-cube
5×pow1 flip3-- associate-/r* flip-- associate-/l*
4×expm1-log1p-u associate-/r/ log1p-expm1-u
2×sub-neg rem-sqrt-square diff-log div-inv associate-/l/
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num
Counts
4 → 155
Calls
4 calls:
10.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
9.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.0ms
(- (exp (* 2.0 x)) 1.0)
7.0ms
(- (exp x) 1.0)

series201.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
90.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
34.0ms
(- (exp (* 2.0 x)) 1.0)
23.0ms
(- (exp x) 1.0)

simplify55.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04801694
115231484
250011470

prune389.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.3b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
5.1b
(fma (- 1.0) 1.0 (exp (+ x x)))
5.1b
(- (exp (* 2.0 x)) 1.0)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
315×times-frac
279×*-un-lft-identity
219×add-sqr-sqrt
137×add-cube-cbrt
95×sqrt-prod
38×distribute-lft-out-- difference-of-squares
33×distribute-lft-out
24×associate-/r/
18×associate-/r*
13×div-inv
11×flip3-+ flip-+
9×add-exp-log prod-diff add-cbrt-cube
6×add-log-exp
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv rem-sqrt-square fma-neg div-exp
2×flip3-- flip-- associate-/l/
1×sub-neg frac-2neg sqrt-pow1 pow1/2 sqrt-div diff-log div-sub clear-num fma-udef
Counts
4 → 281
Calls
4 calls:
14.0ms
(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
16.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
1.0ms
(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms
(- (exp (* 2.0 x)) 1.0)

series328.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
152.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
40.0ms
(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms
(- (exp (* 2.0 x)) 1.0)

simplify126.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
09455898
137705653
250015535

prune867.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
0.2b
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b
(/ (pow x 2) (sqrt 2.0))
0.4b
(/ x (sqrt 2.0))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
246×add-sqr-sqrt
231×times-frac
221×*-un-lft-identity
219×add-cube-cbrt
156×prod-diff
82×distribute-rgt-in associate-+r+ distribute-lft-in
70×sqrt-prod
52×associate-*l*
41×unpow-prod-down
21×add-exp-log
15×div-inv unpow2 sqr-pow
13×add-cbrt-cube
12×associate-/r*
11×associate-/l*
9×unswap-sqr
7×div-exp
6×pow1 fma-def associate-*r* add-log-exp
4×expm1-log1p-u sub-neg prod-exp log1p-expm1-u
3×cbrt-undiv
2×frac-times pow-to-exp flip3-- frac-2neg associate-*r/ pow-exp clear-num flip-- cbrt-unprod difference-of-squares
1×+-commutative flip3-+ pow-prod-down associate-*l/ sum-log *-commutative flip-+ distribute-lft-out--
Counts
4 → 391
Calls
4 calls:
13.0ms
(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
25.0ms
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms
(/ (pow x 2) (sqrt 2.0))
4.0ms
(/ x (sqrt 2.0))

series305.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
66.0ms
(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
61.0ms
(/ (pow x 2) (sqrt 2.0))
51.0ms
(/ x (sqrt 2.0))

simplify70.0ms

Algorithm
egg-herbie
Counts
403 → 403
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013655373
150024187

prune817.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow x 2) (sqrt 2.0))
0.4b
(/ x (sqrt 2.0))
2.6b
(exp (log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
26.1b
(log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
39×sqrt-prod
21×unpow-prod-down
12×add-exp-log associate-/r*
11×associate-/l*
8×add-cbrt-cube
7×unpow2 sqr-pow
6×pow1 log-prod
4×expm1-log1p-u log-div exp-prod div-exp log1p-expm1-u add-log-exp
3×exp-sum
2×cbrt-undiv frac-2neg flip3-+ exp-diff clear-num log-pow flip-+ div-inv
1×pow-to-exp rem-log-exp pow-exp rem-exp-log
Counts
4 → 154
Calls
4 calls:
6.0ms
(/ (pow x 2) (sqrt 2.0))
4.0ms
(/ x (sqrt 2.0))
5.0ms
(exp (log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
4.0ms
(log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ (pow x 2) (sqrt 2.0))
50.0ms
(/ x (sqrt 2.0))
135.0ms
(exp (log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
222.0ms
(log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04571369
117501182
250031145

prune414.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes20.0ms

Accuracy

72.5% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch38.0ms

Steps
ItersRangePoint
5
-7.455527952367615e-16
-3.171438052781698e-16
-7.195205579931451e-16

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04228
14228

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.4s6785×body10240exit
395.0ms12465×body80nan
261.0ms7407×body80valid
59.0ms729×body160valid