Details

Time bar (total: 7.0s)

sample122.0ms

Algorithm
intervals
Results
30.0ms46×body10240exit
24.0ms309×body80valid
23.0ms42×body1280valid
16.0ms48×body640valid
6.0ms26×body320valid
2.0ms11×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(exp (- (* (+ 1.0 eps) x)))
2.4b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
77×exp-neg
76×frac-times
58×neg-sub0 exp-diff
40×associate-*l/
38×associate-*r/
30×flip3-+ flip-+
29×flip3-- flip--
19×un-div-inv
15×add-sqr-sqrt
13×*-un-lft-identity
9×add-cube-cbrt associate-*l*
8×pow1 add-cbrt-cube add-log-exp
7×add-exp-log
6×exp-prod associate-*r*
4×expm1-log1p-u log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in fma-neg diff-log prod-diff neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 170
Calls
4 calls:
23.0ms
(* (- 1.0 eps) x)
53.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
7.0ms
(exp (- (* (+ 1.0 eps) x)))
51.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (- 1.0 eps) x)
45.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
23.0ms
(exp (- (* (+ 1.0 eps) x)))
177.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify153.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013353907
149433603
250013603

prune850.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 1 expressions with local error:

7.4b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series35.0ms

Counts
1 → 3
Calls
1 calls:
35.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify31.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04289
113678
272278
3500275

prune61.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
3.8b
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
7.4b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
4×pow1 add-exp-log add-cbrt-cube
3×expm1-log1p-u pow-unpow log1p-expm1-u add-log-exp
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
3 → 58
Calls
3 calls:
3.0ms
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
3.0ms
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
4.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series133.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
35.0ms
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
35.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify218.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0169545
1620511
24809505
35001505

prune209.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* 12.0 (pow x 2))
7.4b
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
11.6b
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
8×add-exp-log associate-*r*
7×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down unswap-sqr
3×pow1 cbrt-prod expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
2×unpow2 sqr-pow
1×pow-to-exp pow1/3 pow-exp *-commutative cbrt-unprod fma-udef
Counts
3 → 52
Calls
3 calls:
12.0ms
(* 12.0 (pow x 2))
0.0ms
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
1.0ms
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

series202.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(* 12.0 (pow x 2))
35.0ms
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
143.0ms
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0285418
1997377
25001355

prune229.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

regimes124.0ms

Accuracy

96.6% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.5b

bsearch154.0ms

Steps
ItersRangePoint
7
3.704765010127866
357.62882370262366
311.8165880899525

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05529
16529
26529

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.1s1936×body10240exit
949.0ms1702×body1280valid
782.0ms9996×body80valid
457.0ms1310×body640valid
160.0ms663×body320valid
51.0ms333×body160valid