Details

Time bar (total: 6.8s)

sample106.0ms

Algorithm
intervals
Results
29.0ms63×body1280valid
28.0ms70×body10240exit
19.0ms340×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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize17.0ms

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)))))

rewrite30.0ms

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:
9.0ms
(* (+ 1.0 eps) x)
6.0ms
(* (- 1.0 eps) x)
12.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
1.0ms
(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)))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (+ 1.0 eps) x)
28.0ms
(* (- 1.0 eps) x)
48.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
225.0ms
(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)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0462738
11805635
25002628

prune334.0ms

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:
5.0ms
(* 0.5 (pow x 2))
1.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.0ms
(/ (pow x 3) eps)

series97.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 0.5 (pow x 2))
51.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
21.0ms
(/ (pow x 3) eps)

simplify59.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0305506
11561465
25001451

prune265.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
185×times-frac
83×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×add-exp-log
14×cube-mult unpow-prod-down unpow3 cube-prod sqr-pow
13×associate-/r*
12×div-exp
10×div-inv
9×add-cbrt-cube
8×associate-/l*
6×cbrt-prod
4×pow1 expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv
2×pow-to-exp pow1/3 prod-exp
1×frac-2neg clear-num associate-/r/ fma-udef
Counts
4 → 184
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
8.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
1.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

series598.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt x)
170.0ms
(cbrt x)
181.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
70.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify145.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (129.0ms)

IterNodesCost
07211771
143251200
250011152

prune564.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
3.2b
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
11.5b
(log (exp (cbrt x)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×log-pow
6×exp-prod
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod
2×pow1/3
1×rem-log-exp fma-udef
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
3.0ms
(log (exp (cbrt x)))

series596.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt x)
178.0ms
(cbrt x)
76.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
169.0ms
(log (exp (cbrt x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0139339
1329286
21862275
35001275

prune276.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

regimes148.0ms

Accuracy

94.4% (0.9b remaining)

Error of 4.3b against oracle of 3.4b and baseline of 19.3b

bsearch90.0ms

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

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04735
14735

end0.0ms

sample2.9s

Algorithm
intervals
Results
770.0ms1891×body10240exit
767.0ms1749×body1280valid
551.0ms10040×body80valid
317.0ms1224×body640valid
116.0ms680×body320valid
33.0ms305×body160valid