Details

Time bar (total: 5.9s)

sample106.0ms

Algorithm
intervals
Results
31.0ms70×body10240exit
26.0ms63×body1280valid
18.0ms340×body80valid
8.0ms35×body640valid
3.0ms21×body320valid
1.0ms8×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (38.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(* (- 1.0 eps) x)
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
3.9b
(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)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×add-sqr-sqrt
13×add-cbrt-cube
12×add-exp-log
10×add-cube-cbrt
9×associate-*l*
8×pow1
6×associate-*r*
4×expm1-log1p-u times-frac associate-*l/ log1p-expm1-u associate-/l* add-log-exp
3×prod-exp cbrt-unprod distribute-lft-out
2×cbrt-undiv flip3-+ div-exp pow-prod-down *-commutative flip-+ associate-/l/ unswap-sqr
1×flip3-- frac-2neg clear-num associate-/r* flip-- fma-udef div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 84
Calls
4 calls:
10.0ms
(* (+ 1.0 eps) x)
11.0ms
(* (- 1.0 eps) x)
27.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (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)))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (+ 1.0 eps) x)
36.0ms
(* (- 1.0 eps) x)
45.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
241.0ms
(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)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0462738
11805635
25002628

prune353.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
3.2b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.1b
(/ (pow x 3) eps)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×times-frac
31×add-cube-cbrt *-un-lft-identity
16×unpow-prod-down
13×add-exp-log
12×cube-prod associate-/l*
8×associate-*r*
7×add-cbrt-cube
6×sqr-pow
4×cube-mult unpow3 unswap-sqr
3×pow1 expm1-log1p-u div-exp associate-*l* prod-exp associate-/r* log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp unpow2
1×cbrt-undiv frac-2neg clear-num *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 106
Calls
3 calls:
6.0ms
(* 0.5 (pow x 2))
0.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.0ms
(/ (pow x 3) eps)

series101.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(* 0.5 (pow x 2))
48.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
27.0ms
(/ (pow x 3) eps)

simplify66.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0305506
11561465
25001451

prune280.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
3.2b
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
43.3b
(cbrt (pow x 3))
43.3b
(cbrt (pow x 3))

rewrite16.0ms

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:
10.0ms
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
0.0ms
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
1.0ms
(cbrt (pow x 3))
2.0ms
(cbrt (pow x 3))

series173.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
85.0ms
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
16.0ms
(cbrt (pow x 3))
16.0ms
(cbrt (pow x 3))

simplify84.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
0388603
12652494
25002480

prune356.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
3.2b
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
3.8b
(log (exp x))
43.3b
(cbrt (pow x 3))

rewrite163.0ms

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:
10.0ms
(/ (* (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))))
1.0ms
(log (exp x))
2.0ms
(cbrt (pow x 3))

series147.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
79.0ms
(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))

simplify81.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
0432605
12783478
25002464

prune333.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.7b

regimes121.0ms

Accuracy

92.9% (1.1b remaining)

Error of 2.7b against oracle of 1.6b and baseline of 17.4b

bsearch89.0ms

Steps
ItersRangePoint
6
1.0380161377784092e-26
1.091895904028376e-25
1.0640289263225317e-25

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04733
14733

end0.0ms

sample2.9s

Algorithm
intervals
Results
782.0ms1749×body1280valid
763.0ms1891×body10240exit
553.0ms10040×body80valid
310.0ms1224×body640valid
111.0ms680×body320valid
34.0ms305×body160valid