Details

Time bar (total: 6.0s)

sample99.0ms

Algorithm
intervals
Results
26.0ms66×body10240exit
23.0ms54×body1280valid
15.0ms286×body80valid
11.0ms41×body640valid
4.0ms22×body320valid
1.0ms9×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.0b
(exp (* (- 1.0 eps) x))
5.3b
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube
8×add-exp-log
7×add-sqr-sqrt add-cube-cbrt exp-prod
4×pow1 expm1-log1p-u times-frac log1p-expm1-u associate-/l*
3×rem-exp-log
2×cbrt-undiv exp-to-pow div-exp associate-/l/ distribute-lft-out
1×neg-sub0 distribute-lft-neg-in exp-neg neg-mul-1 distribute-rgt-neg-in frac-2neg flip3-+ exp-diff diff-log neg-log prod-exp clear-num associate-/r* cbrt-unprod flip-+ fma-udef div-inv
Counts
4 → 69
Calls
4 calls:
6.0ms
(exp (- (* (+ 1.0 eps) x)))
45.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
8.0ms
(exp (* (- 1.0 eps) x))
0.0ms
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(exp (- (* (+ 1.0 eps) x)))
46.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
21.0ms
(exp (* (- 1.0 eps) x))
233.0ms
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify35.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0365706
11230610
25001590

prune268.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 0.5 (pow x 2)))
0.0b
(* 0.5 (pow x 2))
1.8b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
8.2b
(/ (pow x 3) eps)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×times-frac
34×add-cube-cbrt *-un-lft-identity
16×unpow-prod-down
14×add-exp-log
12×cube-prod associate-/l*
8×associate-*r* add-cbrt-cube
6×add-log-exp sqr-pow
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u unswap-sqr
3×fma-neg div-exp associate-*l* prod-diff prod-exp associate-/r*
2×pow-to-exp pow-exp unpow2
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log clear-num *-commutative flip-- cbrt-unprod fma-udef div-inv
Counts
4 → 126
Calls
4 calls:
6.0ms
(- 1.0 (* 0.5 (pow x 2)))
11.0ms
(* 0.5 (pow x 2))
0.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
9.0ms
(/ (pow x 3) eps)

series161.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- 1.0 (* 0.5 (pow x 2)))
25.0ms
(* 0.5 (pow x 2))
52.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
22.0ms
(/ (pow x 3) eps)

simplify68.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0373633
11839580
25001564

prune324.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
2.2b
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
42.9b
(cbrt (pow x 3))
42.9b
(cbrt (pow x 3))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
24×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log
13×associate-/r*
12×add-cbrt-cube
6×cbrt-undiv unpow-prod-down cube-prod div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv
2×cube-mult pow1/3 unpow3 prod-exp rem-cbrt-cube cbrt-unprod sqr-pow
1×frac-2neg clear-num associate-/r/ fma-udef associate-/l*
Counts
4 → 104
Calls
4 calls:
0.0ms
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
19.0ms
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
2.0ms
(cbrt (pow x 3))
2.0ms
(cbrt (pow x 3))

series171.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
48.0ms
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
15.0ms
(cbrt (pow x 3))
20.0ms
(cbrt (pow x 3))

simplify80.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
0388603
12652494
25001480

prune329.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
1.4b
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
3.6b
(log (exp x))
42.9b
(cbrt (pow x 3))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log
14×add-cbrt-cube
13×associate-/r*
12×cbrt-prod
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log-pow log1p-expm1-u add-log-exp
3×unpow-prod-down log-prod exp-prod cube-prod div-inv
2×prod-exp cbrt-unprod
1×cube-mult frac-2neg pow1/3 unpow3 rem-log-exp clear-num associate-/r/ rem-cbrt-cube fma-udef associate-/l* sqr-pow
Counts
4 → 98
Calls
4 calls:
24.0ms
(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
0.0ms
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
3.0ms
(log (exp x))
2.0ms
(cbrt (pow x 3))

series139.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
73.0ms
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
9.0ms
(log (exp x))
16.0ms
(cbrt (pow x 3))

simplify76.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
0432605
12783478
25002464

prune446.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

regimes77.0ms

Accuracy

96.3% (0.6b remaining)

Error of 2.3b against oracle of 1.7b and baseline of 17.4b

bsearch150.0ms

Steps
ItersRangePoint
10
0.5456674408319693
3845520655822.575
3.5565030670058277

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05434
16034
26034

end0.0ms

sample3.0s

Algorithm
intervals
Results
797.0ms1963×body10240exit
751.0ms1731×body1280valid
559.0ms9978×body80valid
316.0ms1259×body640valid
105.0ms645×body320valid
37.0ms346×body160valid