Details

Time bar (total: 5.1s)

sample92.0ms

Algorithm
intervals
Results
33.0ms54×body1280valid
20.0ms14×body2560valid
10.0ms28×body640valid
10.0ms129×body80valid
6.0ms25×body320valid
1.0ms6×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0117
1137
2137

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize11.0ms

Local error

Found 3 expressions with local error:

7.5b
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.4b
(sin (/ x (* y 2.0)))
29.0b
(tan (/ x (* y 2.0)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×tan-quot
1×cbrt-undiv frac-2neg div-exp clear-num div-inv associate-/l/
Counts
3 → 49
Calls
3 calls:
4.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms
(sin (/ x (* y 2.0)))
1.0ms
(tan (/ x (* y 2.0)))

series103.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
11.0ms
(sin (/ x (* y 2.0)))
50.0ms
(tan (/ x (* y 2.0)))

simplify66.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0146485
1433441
21789441
35001441

prune231.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 26.5b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune39.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 26.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
7.5b
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.4b
(sin (/ x (* y 2.0)))
29.0b
(tan (/ x (* y 2.0)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
5×log1p-expm1-u
4×pow1 expm1-log1p-u add-log-exp
3×associate-/r* associate-/l*
2×tan-quot
1×cbrt-undiv expm1-log1p frac-2neg div-exp clear-num div-inv associate-/l/ expm1-udef
Counts
4 → 60
Calls
4 calls:
0.0ms
(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
4.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms
(sin (/ x (* y 2.0)))
1.0ms
(tan (/ x (* y 2.0)))

series190.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
42.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms
(sin (/ x (* y 2.0)))
47.0ms
(tan (/ x (* y 2.0)))

simplify74.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0178614
1530553
22057551
35001551

prune287.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 26.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow x 2) E)
1.0b
(- E 1)
14.6b
(/ (* (pow x 2) E) (pow y 2))
17.5b
(log1p (fma 0.125 (/ (* (pow x 2) E) (pow y 2)) (- E 1)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
28×add-sqr-sqrt
24×prod-exp
21×*-un-lft-identity div-exp
18×add-cube-cbrt
15×pow-to-exp pow-exp
13×e-exp-1
11×add-cbrt-cube
10×unpow-prod-down
9×prod-diff
8×times-frac associate-*l* associate-/r*
6×add-log-exp
5×expm1-log1p-u
4×pow1 log1p-expm1-u unpow2 unswap-sqr sqr-pow
3×fma-neg associate-*r*
2×cbrt-undiv expm1-def cbrt-unprod difference-of-squares
1×sub-neg log1p-udef flip3-- frac-2neg diff-log difference-of-sqr-1 log1p-expm1 clear-num *-commutative flip-- div-inv associate-/l* distribute-lft-out--
Counts
4 → 127
Calls
4 calls:
7.0ms
(* (pow x 2) E)
4.0ms
(- E 1)
11.0ms
(/ (* (pow x 2) E) (pow y 2))
0.0ms
(log1p (fma 0.125 (/ (* (pow x 2) E) (pow y 2)) (- E 1)))

series196.0ms

Counts
4 → 10
Calls
4 calls:
36.0ms
(* (pow x 2) E)
0.0ms
(- E 1)
42.0ms
(/ (* (pow x 2) E) (pow y 2))
118.0ms
(log1p (fma 0.125 (/ (* (pow x 2) E) (pow y 2)) (- E 1)))

simplify69.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0431676
11958555
25002544

prune326.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 26.4b

regimes309.0ms

Accuracy

0% (2.3b remaining)

Error of 29.1b against oracle of 26.8b and baseline of 29.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010

end0.0ms

sample3.0s

Algorithm
intervals
Results
929.0ms1433×body1280valid
887.0ms661×body2560valid
382.0ms1011×body640valid
333.0ms4008×body80valid
169.0ms603×body320valid
61.0ms284×body160valid