Details

Time bar (total: 8.2s)

sample117.0ms

Algorithm
intervals
Results
32.0ms72×body1280valid
31.0ms73×body10240exit
17.0ms284×body80valid
13.0ms35×body640valid
4.0ms25×body320valid
2.0ms17×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
3.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
32×flip3-- flip--
30×flip3-+ flip-+
23×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac fma-neg diff-log prod-diff distribute-lft-out
Counts
4 → 183
Calls
4 calls:
10.0ms
(* (- 1.0 eps) x)
38.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
32.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
26.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (- 1.0 eps) x)
52.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
45.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
194.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013724120
150013814

prune500.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(- 2.0 (* 1.0 (pow x 2)))
6.0b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×fma-neg prod-diff
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- fma-udef
Counts
2 → 30
Calls
2 calls:
3.0ms
(- 2.0 (* 1.0 (pow x 2)))
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series97.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(- 2.0 (* 1.0 (pow x 2)))
44.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify67.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0126221
1412193
22139191
35001171

prune102.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize15.0ms

Local error

Found 4 expressions with local error:

6.0b
(fma (pow x 3) 0.6666666666666667 (* (* (cbrt (- 2.0 (* 1.0 (pow x 2)))) (cbrt (- 2.0 (* 1.0 (pow x 2))))) (cbrt (- 2.0 (* 1.0 (pow x 2))))))
8.0b
(cbrt (- 2.0 (* 1.0 (pow x 2))))
8.0b
(cbrt (- 2.0 (* 1.0 (pow x 2))))
8.0b
(cbrt (- 2.0 (* 1.0 (pow x 2))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma (pow x 3) 0.6666666666666667 (* (* (cbrt (- 2.0 (* 1.0 (pow x 2)))) (cbrt (- 2.0 (* 1.0 (pow x 2))))) (cbrt (- 2.0 (* 1.0 (pow x 2))))))
1.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))
1.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))
2.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))

series759.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma (pow x 3) 0.6666666666666667 (* (* (cbrt (- 2.0 (* 1.0 (pow x 2)))) (cbrt (- 2.0 (* 1.0 (pow x 2))))) (cbrt (- 2.0 (* 1.0 (pow x 2))))))
238.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))
240.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))
236.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))

simplify109.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0264905
1889839
23730762
35001756

prune279.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize28.0ms

Local error

Found 4 expressions with local error:

7.3b
(cbrt (- (* 2.0 2.0) (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2)))))
8.0b
(cbrt (+ 2.0 (* 1.0 (pow x 2))))
8.0b
(cbrt (- 2.0 (* 1.0 (pow x 2))))
8.0b
(cbrt (- 2.0 (* 1.0 (pow x 2))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
13×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- flip--
1×flip3-+ flip-+ difference-of-squares
Counts
4 → 61
Calls
4 calls:
2.0ms
(cbrt (- (* 2.0 2.0) (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2)))))
2.0ms
(cbrt (+ 2.0 (* 1.0 (pow x 2))))
1.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))
2.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))

series1.7s

Counts
4 → 12
Calls
4 calls:
924.0ms
(cbrt (- (* 2.0 2.0) (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2)))))
190.0ms
(cbrt (+ 2.0 (* 1.0 (pow x 2))))
376.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))
242.0ms
(cbrt (- 2.0 (* 1.0 (pow x 2))))

simplify60.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05421003
12005952
25001931

prune400.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

regimes109.0ms

Accuracy

95.8% (0.7b remaining)

Error of 1.2b against oracle of 0.5b and baseline of 16.8b

bsearch128.0ms

Steps
ItersRangePoint
8
12.952944841197453
4043.3875059490183
177.7594670374271

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04021
14221
24221

end0.0ms

sample3.1s

Algorithm
intervals
Results
830.0ms1856×body10240exit
822.0ms1774×body1280valid
607.0ms9956×body80valid
342.0ms1245×body640valid
124.0ms641×body320valid
36.0ms298×body160valid